Origami/Examples 2

This is the "E:/WikiversityStuff/FoldingWithTheStars.txt" file, which was 
created WED 2012 MAR 28 09:05 PM, 
revised TUE 2012 AUG 07 05:29 PM. 

A much better name for this page would be, "RCB_FoldingWithTheStars". I have asked one of the custodians for help. Ray Calvin Baker (talk) 18:40, 11 August 2012 (UTC)

A friend of mine recently asked me to publish my instructions for folding a simple hopping frog. So, I am "rushing" to add this information, below. As always, making the illustrations is, for me, a VERY slow process. If you do not have patience, you had better find an activity more exciting than origami. Ray Calvin Baker (discusscontribs) 14:46, 4 September 2013 (UTC)

THIS IS A COMPLETELY FRESH UPLOAD (If I must, I can upload it again.),
primarily to break a large lesson plan into more manageable sections. 
(Each section is numbered to facilitate maintenance.) I still need to 
correct some known MISTAKES, and add material and PICTURES to 
incomplete sections. A big hurdle for me is simply to get material 
"out there". After that big step is taken, I can ask the entire 
world to help me with maintaining/correcting/improving it.
This is a wiki, right? :-)

This lesson plan is really about making geometric star-shaped 
decorations. It is not really about dancing with the stars.

Watch out for the sections which are INCOMPLETE! #1 of 23. I'm still working on several of these. There are at least 20 altogether. I found some serious MISTAKES in what I have written so far, so I need to correct those ASAP. I found those while preparing to present this material at the Caroline County Senior Center in Denton, Maryland. I look forward to actually having a CLASS—real, live people interested in some of the decorations and models I know how to make. Interaction and use of this material should help enormously to improve the accuracy and relevance of the information. PICTURES! I need to add lots of pictures, too. I know several ways "how to", but it takes time to create pictures using only PAINT.EXE. The regular pentagon layout diagram is proof that I CAN DO THIS! :-)

Ray Calvin Baker (talk) 21:44, 7 August 2012 (UTC)

Do Folding with the stars!
(even if you have two left feet and need a clock to keep time).
Hopefully, you will be able to sit in a comfortable chair 
next to a suitable work table. You won't even need to work up 
a sweat!

Folding with the Stars -- Improved version -- 
better than Dancing with the Stars -- no losers!
Everybody wins, and every winner takes home a handmade 
(made in USA) trophy -- or several trophies!


Teachers are especially invited! You will be able to share 
important, interesting, educational and cultural activities 
with your classes.

FREE! to the first ten people (any age above third grade) 
who sign up. After ten sign up, others will go on a waiting 
list for a possible follow-up session. Each meeting will 
consist of HANDS-ON activities; be prepared to have some good, 
clean fun! Be prepared to succeed in making something you've 
never before even imagined!

Paper and supplies will be provided.

An entertaining afternoon of unusual, but easy, craft projects 
is planned at the Caroline County Public Library in Greensboro. 
Mathematics only -- no arithmetic allowed, except by request. 
(Do you mean to tell me there is a difference between  
Mathematics and Arithmetic? I most certainly do! Come and find 
out what the difference is.)

Permissions, support, and survey of available 
facilities is needed.
Possible Additional venue -- The Caroline County (Maryland) Senior Center

Activities may include:
Origami (to fold paper)
Storigami (to tell a story, and illustrate it with origami)
Paper Sculpture
Paper Engineering 
and some other useful craft materials

---- ----- ----- ----- ----- ----- ----- ----- ----- -----

Above is a possible plan for the flyer, intended to attract 
attention, and to encourage people to sign up and attend. 


Below is the plan of events. I hope that by posting this 
as a lesson plan at the Wikiversity I can establish some 
credibility for my outrageous claims. This should also allow 
me to post stories, pictures, and diagrams for participants 
to preview, download, and bring with. Of course, anyone on 
planet earth with access to the Wikiversity is free to use 
this material, once I post it.

Since by opening this project to the entire Greensboro 
community (to the entire world, via Wikiversity), I expect 
a wide range of ages, abilities, and prior experience, I 
plan to introduce some of the easiest, most fundamental 
crafts projects. Easy does NOT exclude four-dimensional 
geometry, vector calculus (without arithmetic, as much as 
possible), and discussion of non-orientable surfaces, and 
other topics as they arise. There are many strange, 
unusual, and unexpected things in Mathematics! Emphasis 
will be on hands-on, actual construction of interesting 
models. My goal is to make the "How to Make (Almost) 
Anything" course, popular at M. I. T., (though I have only 
read about it), accessible to a larger and younger audience.

NOTE: More activities must be planned than are expected to be 
actually used at any one event. Also, sometimes one must move 
on to another activity, due to lack of interest, or unexpected 
difficulties. Moreover, once a lesson plan is posted here, it 
is immediately available for anyone who wishes to use it. I 
intend to use the material myself, if there is ever another 
sequel event.

---- ----- ----- ----- ----- ----- ----- ----- ----- ----- 


Part of the beauty and wonder of origami is that NO TOOLS 
(other than the paper itself) are really REQUIRED. However, 
some folders like to use the handle of an ordinary butter 
knife to crease their folds. (If you fold a LOT or origami, 
your thumbnail may get uncomfortably HOT. And, you may wear 
grooves into your nails that interfere with other activities.) 
Scissors or a paper cutter are, of course, necessary to cut 
paper to specific sizes and shapes. (Even some authentic and 
historic Japanese origami sometimes requires cuts or slits 
in the paper.) Toothpicks, skewers, and tweezers are sometimes 
useful to put a stubborn flap into its proper place.

	Paper (almost all kinds -- except paper napkins)
	Knife with smooth handle (and no sharp blade)
	Paper cutter 
	Glue, tape, wire (These supplies are used mostly to 
		stabilize models for long-term display, so 
		they don't unfold themselves and look sloppy.)

---- ----- ----- ----- ----- ----- ----- ----- ----- -----



Inasmuch as not everyone has received the benefits of growing 
up in a family where construction engineering, drafting 
design, and other scientific and technological activities 
were everyday occurrences, I feel it to be necessary to give 
instructions for the preparation of the materials I expect to 

I am planning to bring prepared materials for these special 
projects, in order to allow you to begin working without delay.


Summary of Requirements for Popular Shapes, by shape and 
	by number required (see the source books)
Name			Shape	#	Shape	#	Shape	#
Regular Tetrahedron	3-sides	X 4 
Cube			4-sides	X 6 
Regular Octahedron	3-sides	X 8 
Regular Dodecahedron	5-sides	X 12 
Regular Icosahedron	3-sides	X 20

Truncated Tetrahedron	3-sides	X 4	6-sides	X 4
Truncated Cube		3-sides	X 8	8-sides	X 6 
Truncated Octahedron	4-sides	X 6	6-sides	X 8 
Truncated Dodecahedron	3-sides	X 20	10-sides X 12 
Truncated Icosahedron	5-sides	X 12	6-sides X 20
AKA Soccer ball, AKA Bucky ball 
Cuboctahedron		3-sides	X 8	4-sides	X 6 
Icosadodecahedron	3-sides	X 20	5-sides	X 12
Rhombicuboctahedron	3-sides	X 8	4-sides X 18 
Rhombitruncated		4-sides	X 12	6-sides	X 8	8-sides	X 6 
Rhombicosadodecahedron	3-sides	X 20	4-sides	X 30	5-sides	X 12 
Rhombitruncated		4-sides	X 30	6-sides	X 20	10-sides X 12 
Snub Cube		3-sides	X 32	4-sides	X 6 
Snub Dodecahedron	3-sides	X 80	5-sides X 12

Prisms			n-sides X 2	4-sides X n
Anti-Prisms		n-sides	X 2	3-sides	X 2 X n

Note: Some of these shapes are obviously precursors of the 
geodesic dome, invented by architect R. Buckminster Fuller, 
and featured in some museums of art. I did not make up the 
names of these shapes! But various (allegedly authoritative) 
sources sometimes get some of the names mixed up.


	Ordinary Poster Board (white, or colored, one or both 
		sides. What I get in Mayland, USA, is usually 
		22 inches by 28 inches.)

	Yardstick (or meter stick, if outside United States)
		( I can use my computer to convert 1 inch to 25.4 mm)
	Ball-point Pen, or pencil 



	Turn your measuring stick onto its edge when laying 
	out the dimensions. This puts the graduations on the 
	measuring stick closer to the poster board, which 
	should improve the accuracy of your lay out.

	Sight down along the edge of your straight-edged 
	measuring stick to be sure that it really is straight. 
	You want to draw straight line segments, not curves.

	The taper of a ball-point pen or a sharpened pencil, 
	when held against the straight-edge, leaves a small 
	gap between the edge of the straight instrument and 
	the location of the line which will be drawn. This 
	small gap is good; it helps prevent smearing of ink, 
	if you use a pen. But you will need to estimate the 
	size of this gap, carefully and accurately, in order 
	to draw the lines exactly where you want them to be.

	Clamp the straight-edge FIRMLY against the poster 
	board with one hand. You do NOT want it to move as 
	you are drawing the lines. With the pen or pencil 
	held in the other hand, far enough above the poster 
	board so as to leave NO MARK, practice a few times 
	making a smooth, sweeping stroke, while letting one 
	finger gently touch the guiding edge. After you gain 
	confidence that you can make a smooth, sweeping 
	stroke with a comfortable movement of your entire arm, 
	lower the pen or pencil to touch the poster board, 
	RELAX, and draw your first line. If that line looks 
	good: smooth, straight, and well-positioned, continue. 
	If it doesn't look so good, take a deep breath, try 
	to figure out what went wrong, reposition your 
	straightedge, clamp, RELAX, practice for a smooth 
	stroke, and try again.

	After a few years, all of these hints will become 
	automatic for a skilled draftsman. But you probably 
	want to help your kids with their homework THIS WEEK. 
	So, I try to share all these hints with you. Relax! 
	If you can cut the pieces accurate within a sixteenth 
	of an inch, you are doing very well, indeed.

	I have calculated (there goes my ban on arithmetic!) 
	dimensions to make many of the shapes, to the nearest 
	quarter of a sixteenth of an inch, in hopes of making 
	it easier for you to lay out these shapes.
	(I have also calculated the metric dimensions to use.)

	The same materials and tools are used for making all 
	of these shapes.

	Note: You will want to use regular poster board, that 
	you can easily cut with ordinary scissors. I am using 
	poster board, because I need to make a lot of these 
	shapes, and poster board (in various colors) looks a 
	lot nicer for public presentation than a wonderful 


	Salvage the cardboard from cereal boxes, snack boxes, 
	and other sources. Throw them away if they are 
	stained by garbage, but keep and use them if they are 
	clean and dry. Cut the boxes along the seams, so they 
	can lay flat for storage. The back side is usually a 
	plain gray or light brown color; ball-point pen ink 
	shows up well to mark your lines for cutting out shapes. 
	It's FREE, (or at least, already paid for), readily 
	available, and ecologically GREEN! Once upon a time 
	(decades ago, before TV became popular), packagers 
	would print designs intended for paper engineering 
	and paper sculpture on their boxes, to be cut out and 
	assembled into model cars, and trains, rockets, and 


	As you disect boxes to salvage the cardboard, you also 
	have an unusual opportunity to explore the many ways 
	professional packaging engineers have solved problems 
	important in manufacturing and commerce. Some boxes 
	are stapled together, some are die-cut, with flaps 
	and slots which lock tother, but most boxes are glued.

	Interesting problem: In how many ways can you unfold 
	a cubical box? Kunihiko Kasahara uses many of these 
	ways in his famous "Panorama Cube", as published in 
	_Origami_Omnibus:_Paper-folding_for_Everybody_, Japan 
	Publications, Inc., Tokyo, New York, {{ISBN|0-87040-699-X}},
	(paperback 384 pp.). This book also contains his 
	instructions for folding modules to make ALL of the 
	regular and semi-regular using only origami folding 

	Most boxes for commercial packaging are also printed, 
	often in may colors. You were probably taught in 
	school that the "primary colors" (for SUBTRACTIVE color 
	mixing) are red, yellow, and blue. These colors work 
	fairly well, for painting posters, but did you know 
	that professional printers usually use magenta, yellow, 
	cyan, and black inks? (OK. so they sometimes call 
	these colors "process red", "process yellow", 
	"process blue", and black. Still they refer to a "MYCK" 
	color system.) You will find their calibration marks 
	and the symbols used to align high speed printing 
	presses, printed in magenta, yellow, cyan, and black 
	ink on many boxes, if you look for them.

	Speaking of colors, your computer monitor uses a 
	different color system -- ADDITIVE color mixing. 
	The primary colors used for this are red, green, 
	and blue. Red and green, added together, make yellow, 
	which is the color of one of the inks used by printers. 
	Green and blue add to make cyan, and red and blue add 
	to make magenta. People who use computer monitors or 
	color television equipment often use these names for 

	Poster board (Do NOT try to use foam-core board for 
	these projects!)

	Ball-point pen, or pencil


	Squares make a regular tessellation, so this should 
	be easy and obvious. I can usually trust the corners 
	of machine-made poster board to be accurate 
	90 degrees angles (i. e., square).

(1) Be sure to measure from the same short side each time when 
you make evenly spaced marks one inch (25.4 mm) apart along each 
long side of the poster board. 
(2) Be sure to measure from the same long side each time when 
you make evenly spaced marks one inch (25.4 mm) apart along each 
short side of the poster board.


	+------------+		+------------+	Do you see 
	|    |    |  |		|    |    |  |	the difference?
	|            |		|            |	Do you 
	|            |		|            |	understand 
	|    |    |  |		|  |    |    |	why it is 
	+------------+		+------------+	important?

The above instructions will be important for many other projects 
which require the laying out of grids.

	|  |  |  |  |  |
	+--+--+--+--+--+	You are trying
	|  |  |  |  |  |	to make a grid,
	+--+--+--+--+--+	something like
	|  |  |  |  |  |	this, only much 
	+--+--+--+--+--+	more extensive.
	|  |  |  |  |  |

(3) Connect all of the marks by drawing parallel line 
segments, as indicated in the diagrams above.
(4) Cut the poster board into strips along the lines you have 
(5) Cut each strip into squares.

	A piece of poster board 22 inches by 28 inches 
	should make 616 1-inch squares.


	Although triangles and hexagons each make regular 
	tessellations, I prefer to use a semi-regular 
	tessellation which includes both shapes instead; 
	this makes it so much easier to cut out the hexagons.

	a            b                   f           d
	.            ________________________________.
	            /    \  /    \  /    \  /    \  /
	           /      \/      \/      \/      \/
	          /\      /\      /\      /\      /
	        /    \  /    \  /    \  /    \  /
	       /      \/      \/      \/      \/
	      /\      /\      /\      /\      /\
            /    \  /    \  /    \  /    \  /    \
	   /      \/      \/      \/      \/      \
	  /\      /\      /\      /\      /\      /\

	It is easy to make angles of 30 degrees and 
	60 degrees with a yardstick or ruler, when 
	you know how. In the diagram above, line 
	segment "bc" should be 6 inches long. To 
	construct this line segment, measure off 
	3 inches from the corner at "a".

	Note: This diagram is intended only to show 
	the princples of the construction! You will 
	achieve more accurate angles if you use longer 
	baselines. I suggest "ab" should be 12 inches 
	(or 30.48 centimeters), and "bc" should be 24 
	inches (or 60.96 centimeters). In any case, 
	you want the edges of the shapes you finally 
	cut out, to be 	one inch (or 2.54 centimeters) 

	Mark point "b" with a pen or pencil. Keeping 
	one of the graduations of the yardstick at 
	point "b", swing the yardstick (or meter stick) 
	until you find point "c", 6 inches away, at the 
	edge of the poster board. Now you can draw line 
	segment "bc". Mark off equal 1-inch (2.54 mm) 
	intervals along this line segment. Mark off 
	equal 1-inch (25.4 mm) intervals along the edge 
	"abfd" of the poster board. Measure length "ac", 
	then mark point "e" at that same distance from 
	edge "abfd". Now you can draw line segments 
	"ce" and "ef", then mark off equal 1-inch 
	(25.4 mm) intervals along each line segment. 
	This should give you enough grid points to 
	cover the poster board with triangles and 
	hexagons. Note: all lines should be parallel 
	to the edge "abfd", to line segment "bc", 
	or to line segment "ef".

	Once the grid is drawn, you can cut strips 
	of hexagons and triangles. Trim off all of 
	the triangles from each strip, and you 
	should be left with a pile of hexagons, and 
	another pile of equilateral triangles.

Yield: [ INCOMPLETE #3 of 23 -- RCB ] YIELD
	I got [ ?? -- RCB ] hexagons and [ ?? -- RCB ] equilateral 
	triangles from my sheet of poster board. There 
	was some scrap near the edges of the sheet.


	Although the above polygons nest together to 
	form space-filling tessellations, regular 
	pentagons cannot fit closely together.

	There will be gaps between these and all of 
	the following shapes. I think that the 
	easiest way to make a lot of these shapes 
	is to first make a grid of carefully 
	calculated measured rectangles, then connect 
	the grid points with line segments which 
	outline the desired shapes. You have already 
	used this method once; since a network of 
	rectangles is also a network of squares, if 
	the dimensions are correct. I will do the 
	rest of the (ugh!) arithmetic for you, or 
	show you ways to avoid most of the arithmetic.

After some experimentation, I was able to upload my first picture into Wikimedia Commons. Here it is!

Layout for a grid of Regular Pentagons

Example Calculations: 
	(You may skip down to "Procedures", if trigonometry 
	scares you. I'm trying to be a counter-terrorist, 
	myself.) There is an incredible irony here! I know 
	a very easy way to arrive at the measurements 
	without arithmetic, but I have a computer instead 
	of a drafting table and instruments. (Hey! I'll 
	keep the computer!) That very easy way (without 
	arithmetic) is simply to make a scale drawing 
	(using a protractor and a ruler) of a pentagon, 
	and measure the relevant dimensions.

	 |   _-  |\    |	This diagram of a regular 
	 |_-     | \   |	pentagon is about as good as
	B+-------|--\--+	I can make it in text mode.
	 |       |   \ |	Computer graphics is an
	 |       |    \|	enormously complicated 
	m+-----+-+-----+D	subject which I prefer 
	 |     O |f   /|	to postpone until some
	 |       |   / |	later time. 
	 |  -_   | /   |
	 |     -_|/    |	This is diagram one, 
	h+-------+-----+k	which will be mentioned 
	         E 		below.

	This diagram will serve for the purpose of
	being an example for the calculations,
	whose results follow. It also indicates 
	how the outline of the regular pentagon 
	will fit on the grid you will construct.

	We want line segment "AB" to be 1 inch 
	(or 2.54 centimeters metric). Point "O" is 
	supposed to be the center of our pentagon.	360 / 5 = 72
	Angle "AOB" is one fifth of a circle, or 72 
	degrees. Half of this angle is 36 degrees.	72 / 2 = 36 
	Let "m" be the midpoint of line segment "AB".
	Then angle "mOB" is 36 degrees, angle "BmO" 
	is 90 degrees, and line segment "mB" is 1/2 
	inch (or 12.7 mm, if you are using metric 
	90 18_-  |\54 90	Let's see if I can emphasize 
	 |_-  54|54\   |	the important angles.
	B+54    |   \36+
	 | -_ 72|    \ |	360/5 = 72
	 | 36-_|72  54\|
	m+-----+-------+D 	180 - 72 = 108
	 | 36_-O72  54/|
	 | _- 72|    / |
	A+_54   |   /36+	108 / 2 = 54
	 |72-_54|54/   |
	 90  18-_|/54 90	90 - 54 = 36

	Line segment "mOfD" is supposed to be a 
	horizontal diameter of the circle with 
	center "O", which passes through all
	five vertices of the desired regular 
	pentagon, and is a line of symmetry.

	This is enough information to apply 	Length("Bm")/Length("mO")
	elementary trigonometry (tri = three, 	= tangent(36 degrees)
	gono = angle, metry = measure), to 
	calculate other measurements of the 	Length("mO") =
	triangle "BOm".				Length("Bm")/tangent(36)

	Having emphasized the angles and the 
	triangles, (and having thouight for 
	several days about how best to provide 
	this information), I find that the 
	relevant facts are these:

	      H * cos(18)
	H *  |90     18_-
	sin  |      _-
	(18) |72_-  H

	(1) Right triangle "BCg" has acute angle 
	18 degrees and hypotenuse H = 1 inch 
	(25.4 mm). Elementary trigonometry (this 
	is what I was searching for) gives 
	Length("gC") = Length("BC") * cosine of 
	18 degreees. I also found that Length("Bg") 
	= Length("BC") * sin of 18 degrees.

	H * sin(18)
	  \      |
	   \     | H *
	    \    | cos
	   H \   | (18)
	       \ |

	(2) Right triangle "CDg" has acute angle 
	36 degrees and hypotenuse H = 1 inch
	(25.4 mm). Then Length("Cj") = Length("CD") 
	* sin (18 degrees), and Length("Dj") =
	Length("CD") * cosine(18 degrees).

	A quick little QB64 BASIC program gives 
	the measurement numbers we want to mark.




Pi = 4.0 * ATN(1.0)
' Computers and calculus students have an easier time calculating
' trigonometric functions when the angles are expresed in radians.
' Multiply the angle by Pi / 180 to convert degrees to radians.
PRINT "Pi ="; Pi

PRINT "This program calculates dimensions for grid to make regular pentagons. "
PRINT "16 * cos(36); 16 * sin(36):"
PRINT 16 * COS(36 * Pi / 180)
PRINT 16 * SIN(36 * Pi / 180)
PRINT "16 * cos(18); 16 * sin(18):"
PRINT 16 * COS(18 * Pi / 180)
PRINT 16 * SIN(18 * Pi / 180)
PRINT "(Dimensions in sixteenths of an inch.)"
PRINT "25.4 * cos(36); 25.4 * sin(36):"
PRINT 25.4 * COS(36 * Pi / 180)
PRINT 25.4 * SIN(36 * Pi / 180)
PRINT "25.4 * cos(18); 25.4 * sin(18):"
PRINT 25.4 * COS(18 * Pi / 180)
PRINT 25.4 * SIN(18 * Pi / 180)
PRINT "(Dimensions in millimeters.)"


Pi = 3.141593
This program calculates dimensions for grid to make regular pentagons.
16 * cos(36); 16 * sin(36):

16 * cos(18); 16 * sin(18):
(Dimensions in sixteenths of an inch.)

25.4 * cos(36); 25.4 * sin(36):

25.4 * cos(18); 25.4 * sin(18):
(Dimensions in millimeters.)

	But it was so much easier just to make 
	the scale drawing and measure off the
	dimensions I wanted! Here is a picture!

Layout for Grid of Regular Pentagons
	Here is how to find the necessary dimensions
	(1) Tape a piece of paper to your drawing board.
	(2) Using your T-square pressed against the edge 
	of the drawing board as a guide, draw a horizontal 
	line near the middle of your paper. 
	(3) Using a drafting triangle, (pressed against the 
	T-square, which is still pressed against the edge 
	of your drafting table) as a guide, draw a second 
	line near the center of your paper, perpendicular to 
	the first line you drew.
	(4) Put the center of your protractor over the 
	intersection of the two lines. Align the 0 and 180 
	degree marks with the first line you drew on your 
	(5) Using the aligned protractor, put a mark at 72 
	degrees. Then, put another mark at 144 degrees. 
	(6) Turn the protractor 180 degrees, then re-align it. 
	(7) Make two more marks, at 72 and 144 degrees.	
	(8) Now, using a straightedge as a guide (a straight 
	side of your drafting triangle will do nicely), draw 
	four line segments which connect the marks you made
	with the protractor, to the intersection of the first 
	two lines you drew (Where the center of the protractor 
	(9) Make two marks 1/2 inch (12.7 mm) from the first 
	line you drew (one mark on each side.). 
	(10) Using your T-square as a guide, draw two new 
	lines, parallel to the first line you drew. These lines, 
	1 inch (25.4 mm) apart, establish the size, or scale, 
	of the regular pentagon you are constructing. They
	intersect the lines you drew at 144 degrees at points 
	"A" and "B" per diagram one.
	(11) Use your drafting compass to draw a circle through
	points "A" and "B", having its center at the 
	intersection of the first two lines you drew. 
	This will establish points "C", "D", and "E", 
	according to diagram one.
	(12) Now that you have located the five vertices of your 
	regular pentagon, connect them by drawing line segments 
	"AB", "BC", "CD", "DE", and "AE". 
	(13) Complete your drawing of the rectangle "gjkh" about 
	regular pentagon "ABCDE". Measure the parts of this 
	rectangle, then use these dimensions to lay out your 
	grid on your poster board.

	After you find the answer to a problem, 
	sometimes you wonder why it took you so 
	long to find the answer!

Information summary:

	What's in the diagram	US Measure 	Equivalent Metric measure

	Length("gB")		5/16 inch	7.85 mm   Measure off these
	Length("Bm")		8/16 inch	12.7 mm   distances along 
	Length("mA") = "Bm"	8/16 inch	12.7 mm	  one edge of your
	Length("hA") = "gB" 	5/16 inch	7.85 mm	  poster board.

	Length("gC")		15.25/16 inch	24.16 mm   Measure these along
	Length("Cj")		9.5/16 inch	14.92 mm   perpendicular edge.


	(1) Measure off and mark the four lengths "gB", "Bm", 
	"mA", and "hA" along one edge of your poster board. 
	(2) Repeat step (1), until you have marks all along 
	one edge of your poster board. 
	(3) Repeat steps (1) and (2) all along the opposite 
	edge of your poster board. 
	(4) Connect corresponding marks with a series of 
	parallel line segments. (I recommend using a long 
	straightedge to draw these lines.)
	(5) Two edges of your poster board have not been 
	marked yet. Along one of these edges, measure off and 
	mark the two lengths "gC" and "Cj". 
	(6) Continue measuring and marking lengths "gC" and "Cj",
	all along the edge you have started marking. 
	(7) One edge of your poster board has not been marked yet. 
	Use lengths "gC" and "Cj" to mark this edge.
	(8) Connect corresponding marks with a series of 
	parallel line segments. (I recommend using a long 
	straightedge to draw these lines.) 
	(9) Use a short straightedge as a guide to draw all five 
	sides of each regular pentagon in your grid.
	(10) Cut your poster board into strips, so that each 
	strip contains an entire row of regular pentagons. 
	(11) Cut each strip into rectangles, so that each 
	rectangle contains a regular pentagon.
	(12) Trim each rectangle. Keep all of the regular 
	pentagons. Discard all of the triangular scraps.

Yield:	[ INCOMPLETE #6 of 23 ] YIELD
	I got [ ?? -- RCB ] regular pentagons from my sheet of 
	poster board. Some scrap had to be trimmed from each 


	+m    +-------+    n+	Note: This diagram is
	     /C       D\     	distorted. (It's too
	    /           \    	tall.) Technical 
	   /             \   	difficulties such as
	  /               \  	this often arise when 
	 /                 \ 	one tries to push
	+B                 E+	equipment beyond the
	|                   |	limits for which it
	|                   |	 was designed . Word 
	|                   |	processors were never 
	|         O         |	designed for making 
	|                   |	diagrams. But creative 
	|                   |	thinking often requires 
	|                   |	that one thinks beyond 
	+A                 F+	the normal limits. 
	 \                 /
	  \               /  	This shape has four-fold 
           \             /   	rotational symmetry, so 
	    \           /    	a lot of the lengths in 
	     \H       G/	the diagram are identical.
	+q    +-------+    p+

	Angle "mBC" is supposed to be 45 degrees. A true 
	scale diagram, or trigonometric calculation, would 
	establish this as a fact. Triangle "mBC" is thus 
	an iscoceles right triangle, with some interesting 
	and unusaul properties. If Length("BC") = 1 inch 
	(25.4 mm) then length("mC") = length("mB") = 
	cosine(45 degrees) = sine(45 degrees) = 1/2 the 
	square root of 2 = 0.7071.

Table of measurements:
	Length("mB") = Length("mC")	11.25/16 inch	(17.96 mm)
	Length("AB") = Length("CD")	1 inch		(25.4  mm)
	Length("qA") = Length("Dn")	11.25/16 inch	(17.96 mm)

	(1) Measure off the dimensions for one cell of the grid
	along one edge of your poster board. 
	(2) copy these measurements along the edge to make as 
	many grid cells as possible along that edge. 
	(3) Repeat steps (1) and (2) along each of the other 
	three edges of your poster board. (Remember to start 
	all of your measurements from the correct edge of the 
	poster board.) 
	(4) Use a long straightedge as a guide to draw line
	segments connecting corresponding measured marks.
	(5) Cut your poster board into strips along the 
	grid lines you have drawn. 
	(6) Cut each strip into squares along the grid lines. 
	(7) Trim away the triangles from each square. 
	(8) Discard the triangular scraps.

Yield:	[ INCOMPLETE #7 of 23 ] YIELD
	Four triangles of scrap had to be trimmed from each square 
	to make [ ?? -- RCB ] regular octagons -- "stop signs".


	The computations for laying out the grid for this shape 
	are somehat like the process for laying out the regular 
	pentagons, except for the essential fact that there are 
	twice as many sides for this 10-sided shape.

Table of measurements:



[ INCOMPLETE! #8 of 23 -- RCB ] YIELD

	None of the regular or semi-regular polyhedra 
	require this shape, but it can be used nicely to 
	make a pretty semi-regular tessellation, prism, 
	or anti-prism, so I try to include a few instances 
	of this shape.

Table of measurements:



[ INCOMPLETE! #9 of 23 -- RCB ] YIELD


On top of everything else, I messed up the numbers. Easy fix! Ray Calvin Baker (talk) 21:06, 9 August 2012 (UTC)


	  c   c   c   c   c
	  /\  /\  /\  /\  /\         
	 \  /\  /\  /\  /\  /\      
	   \  /\  /\  /\  /\  /     
	    \/  \/  \/  \/  \/
	     d   d   d   d   d

This diagram needs an explanation! and further instructions.

It is a good idea to put together as much of a model as you can on a flat surface, such as a table. This allows you to apply maximum pressure to taped or glued joints, to make a stronger model.

[1] < - - Click there to see 20 Equilateral Triangles assembled.

Here is an animated, stereoscopic picture (3-D, if you know how to look at such images. If you have experience with the once-popular "Magic Eye" pictures, then you know how to do this.),which I found in Wikimedia Commons. It illustrates how the above diagram should be assembled. Wikimedia Commons used a slightly different "net", but the assembly principles are the same. Ray Calvin Baker (talk) 00:37, 10 August 2012 (UTC)


	The special tool you will want for this project is 
	a loop of wire which will fit through a drinking 
	straw, to pull a length of string through the straw.

	Wire (light gauge doorbell hookup wire from a 
		hardware store works just fine)

	Wire cutters
	Pliers (needle-nosed pliers work best)
	Ball-point pen or pencil

	(1) Measure off a piece of bell wire about 50 per cent 
	longer than a drinking straw. (Drat! More of that 
	(2) Form a loop at each end of the piece of wire, 
	using the needle-nosed pliers. DON'T POKE YOUR EYE OUT! 
	To minimize the danger of that, I recomment a loop 
	at each end of the piece of wire.
	(3) Twist the short end of the loop around the wire 
	several times. Do this with each of the two loops. 
	(4) Squeeze each loop down to size, so that it will 
	fit easily through the drinking straws, while keeping 
	the loop large enough to slip a piece of string through it. 


Still fixing the numbers! Ray Calvin Baker (talk) 21:08, 9 August 2012 (UTC)


	Take one sheet of paper 8+1/2 inches by 11 inches for 
	each star you wish to make.

	Ball point pen or pencil

	The end of a ruler or yardstick sometimes gets battered 
	and worn, and may not be well aligned with the graduations
	of the measuring instrument. To avoid these possible 
	errors, I usually align the 1-inch mark with the place from 
	which I wish to measure. This can cause its own type of 
	errors, but it is usually easy to spot and fix if your
	measurements are off by exactly one inch.

	(1) Align your ruler with the 1 inch mark at the edge of the
	paper. Mark along both of the short edges at 3 inches, 
	at 5 inches, at 7 inches, and at 9 inches. This will 
	leave 1/2 inch of waste along the long edge. 
	(2) Align your ruler with the 1 inch mark at the edge of the
	paper. Measure and mark along the long edges at 4+1/2 
	inches, at 8 inches, and at 11+1/2 inches. (I avoid using 
	a hyphen in mixed numbers like these; it can too easily be 
	mistaken for a "minus" sign, leading to subtraction instead 
	of addition.) This process of measuring and marking will 
	leave 1/2 inch of waste along the short edge. 
	(3) Using the ruler as a straight-edge, draw line 
	segments to connect the marks. There should be four 
	lines running the long way, and three lines running 
	the short way. 
	(4) Cut the paper along the lines.

	Twelve paper rectangles, each 2 inches by 3+1/2 inches, 
	sufficient to make one Kepler's Star.

I was so amazed that the proportions for this project worked 
out within a sixteenth of an inch, that I wondered if 
variations of this folding technique would work. I found two 
more stars that make very nice decorations.

Several other types of stars (Projects VI. and VIII., as 
described below) can be constructed using variations of the 
techniques used to make Kepler's Star. Instructions for 
preparing the paper for these stars is fully described below, 
as an essential part of these additional projects.

Materials for all other projects are so basic, and no special 
tools are required. so instructions given for all of the other 
projects should be sufficient and complete, as described 

---- ----- ----- ----- ----- ----- ----- ----- ----- ----- 

16. MAKING 3-D SHAPES edit

I'll get there someday, even if I need to take baby steps. Ray Calvin Baker (talk) 21:12, 9 August 2012 (UTC)

	I. MAKING 3-D SHAPES (Paper Sculpture)

Although this is the simplest activity, even graduate students 
at George Washington University found it extremely interesting 
when I shared it with them.

Cardboard shapes (carefully measured and cut out, each side 
about one inch long)
	Equilateral triangles
	Regular pentagons, hexagons, octagons
	Regular ten- and twelve-sided shapes 
	(Consult the source books to estimate
	the numbers required for each shape.) 
	Instructions and hints for making these are given above. 
Masking tape
Illustrations of the five regular and thirteen semi-regular 
(These may be compared with the three regular and eight 
	semiregular tessellations)

Scissors (to cut the masking tape)

Source books:
Ball, W. W. Rouse and H, S. M. Coxeter, _Mathematical_
	_Recreations_and_Essays_ (Thirteenth Edition), 
	Dover Publications, Inc., 1987, ISBN 
	0-486-25357-0 (pbk.) 
Fuse, Tomoko, _Multidimensional_Transformations_Unit_
	_Origami_, Japan Publications, Inc., 1990, 
	{{ISBN|0-87040-852-6}} (pbk.)
Wells, David, _The_Penguin_Dictionary_of_Curious_and_
	_Interesting_Geometry_, Penguin Books, ltd., 
	London, 1991, {{ISBN|0-14-011813-6}} (pbk.)

Make the materials and tools available to the students. 
Construct a simple shape, such as a cuboctahedron, by 
sticking the necessary pieces together with squares of 
masking tape. During construction, show that 
parts of the structure can lie flat, until other parts 
are added, requiring that folds be made to allow the 
developing structure to take its final three-dimensional 
shape. Compare the final shape with its descriptive diagram.

Instruct the students to 
(1) select the shape they would like to build, 
(2) gather the necessary pieces, 
(3) cut squares of masking tape, and 
(4) assemble their model.

Inexperienced students may need to select additional pieces 
and cut additional masking tape. Accuracy in making the 
necesssary estimates comes with experience. Encourage 
cooperation: for example, one student may cut masking tape 
for several other students, with the understanding that he 
will receive help later, in building his own model. Note to 
helpers: Be a helper; don't "take over" someone else's model. 
Although neatness is commendable, any model which holds 
together and allows the student to see the relationships 
between the descriptive diagrams and the final, intended 
shape should be instructive. As time permits and interest 
persists, and supplies last, students may gain proficiency 
by building several models.


One step at a time. Ray Calvin Baker (talk) 21:14, 9 August 2012 (UTC)

This is an open-ended activity, which COULD lead from the 
regular and semi-regular tessellations, and the regular and 
semi-regular polyhedra, prisms and anti-prisms, to the four 
Kepler-Poinsot polyhedra, to five more convex deltahedra, 
to 53 additional uniform polyhedra,  to 92 convex polyhedra 
with regular faces, not to mention compound polyhedra and 
other stellated polyhedra. There is a LOT of territory 
here, not all of it well known or thoroughly explored. 
And then, many of these can be used in the constuction 
of polytopes, of which there are 16 regular polytopes, etc. 
After all that, I'm sure I missed a few. And there are some 
of these shapes which I have never yet seen myself.

Some shapes may be rigid enough to leave some "windows" -- 
places where you deliberately do not tape in a shape. Instead, 
put a small knick-knack or an origami bird, flower, or angel
into your model for a different way to display your folding 

If this activity is going well, I may be able to demonstrate 
a few simple, traditional folds that create sequences of origami 
models, while some students are completing their paper 
sculptures. One example of this is "the multi-fold", which 
includes the oldest documented paper fold in Western culture, 
"Pajarita, the little Spanish bird". Another example is 
"the salt cellar" (formal title), which changes from 
"cootie catcher" to "the lover's knot", to "anvil", "sawhorse", 
and "crown". Another sequence, based on the "triple blintz fold", 
includes "perfume vial", "Japanese lantern", "Yokosan", and a 
"cross". Historically, such sequnces have inspired several 

---- ----- ----- ----- ----- ----- ----- ----- ----- -----


18. A BOX WITH LID edit

1 -- 2 -- 3 -- The Wikiversioty is free! but not yet free of all my stupid mistakes. Still Working! Ray Calvin Baker (talk) 21:17, 9 August 2012 (UTC)

	(storigami: "Brothers Tall and Brothers Short")

Historical Note: [ INCOMPLETE #11 of 23 -- RCB ] SEE "The Paper"
I made up my own poem for this project. But the essential idea was 
mentioned in ----- [source needed]

Two sheets of 8+1/2 inch by 11 inch paper
	(One sheet for the box, one sheet for the lid)

Source book:
Sakoda, James Minoru, _Modern_Origami_, Simon and Schuster, 
	New York, NY, 1969, {{ISBN|0-671-20355-X}} (pbk.)

Since this is "storigami", the paper folding is intended to 
illustrate the story. The words of the story contain 
important clues concerning the sequence of folds, and the 
appearance of the paper after each fold (or series of folds).

	"Brothers Tall and Brothers Short"

(Stage directions -- instructions how to fold and display the 
paper -- are included between a pair of parenteses, like this. 
The actual story is enclosed in quotation marks. 
Give each student two sheets of ordinary 8+1/2 inch by 11 
inch paper. Invite them to watch carefully, and try to fold 
along, as the story is told. Try to pace the story, and 
intervene as necessary, so that no one gets left behind. 
This story is told in a way which will help everyone remember 
the essential steps. Adults and older children should find 
that the boxes with lids are extremely useful for storing 
household items, and items for hobbies and crafts.)

"This is the story of the Brothers Tall, 
Who didn't like extras creases at all."

[ INCOMPLETE #12 of 23 -- RCB ] Illustrations are needed, if possible.

(Place a single sheet of paper on the table in front of you, 
with the long edges running from left to right. 
Pick up the nearest edge, and place that edge exactly over 
the farthest edge. The paper should roll smoothly into a 
cylinder-like shape. Gently and carefully flatten the cylinder.
Make a single length-wise crease down the middle of the 
sheet of paper. This is a valley fold.

Note FYI: The first six creases, as described in the following 
steps, should all be valley folds, all facing upwards.

Lift your creased paper up off the table, and display the 
Brothers Tall. Let your imagination fill in the picture of 
the two brothers. Since this is the first crease, there are 
NO extra creases whatsoever, which the Brothers Tall dislike 
so much.)

"And they lived in a plain, long tent, 
To save money on rent."

(Display the plain, long tent shape formed by one crease. 
The tent shape clearly demonstrates that what is a valley 
fold on one side of the paper, is a mountain fold on the 
other side.)

"Each fell in love with a girl from next door; 
Soon they were married, now there are four."

(Make two more long creases to meet the previous crease 
in the middle. Note: When making the lid, leave a gap about 
the size of these words: "It is OK". Lift the paper to 
display the two couples. Let imaginations fill in the 
features of these two lovely couples.)

"They moved into a plain, long house, 
Because each had a spouse."

(Display the long house shape formed by the three parallel 

"When they went to the cupboard, the cupboard was bare.
There weren't even any shelves in there!"

(Hold the paper so the creases are all vertical. Open and 
close the cupboard doors. Notice that there are no shelves, 
because there are no extra creases.)

"That was the story of the Brothers Tall,
Who didn't like extra creases at all.
So short! So sad! Don't cry or make the paper wetter.
Just place it on the table, and give it a turn, 
I hope, a turn for the better."

(Place the paper flat on the table, then rotate it 90 degrees. 
This is the "turn for the better".)

"This is the story of the Brothers Short, 
Who liked to wear stripes just for sport."

(Make a single crease down the middle of the paper. This crease 
should cross the three creases left from the previous story. 
Let imaginations fill in the picture of the Brothers Short, 
but point out that the stripes are real -- the creases.)

"They lived in a short, striped tent,
To save money on rent."

(Display the short tent form, with its stripes.)

"Each fell in love with a girl from next door.
Soon they were married; now there are four."

(Make two more short creases to meet the short crease in the 
middle. When making the lid, leave a gap about the size of 
these words: "It is OK". Notice that the girls like stripes, 
too. What lovely couples!)

"They moved into a short, stiped house,
Because each had a spouse."

(Display the shape of the short, striped house.)

"They went to the cupboard; each shelf was filled with stuff.
Plenty of stuff, and plenty's enough."

(Hold the paper so that the three short creases are all 
vertical. Open and close the cupboard doors. The shelves 
are real (they are the creases left from the first part 
of the story), but you'll have to imagine the "stuff".)

"With enough in the cupboard, each family begins.
Soon each mommy is the mother of twins. 
Pick up each corner, and fold to the line,
You've done it just right, you've done it just fine.
Now pull up the blanket, over their toeses, 
Until all that sticks out is the tips of their noses. "

(Follow the instructions. My, what big noses these children 

"Turn everything 'round; the paper spins, 
so the other mommy can see both of HER twins.
Pick up each corner, and fold to the line,
You've done it just right, you've done it just fine.
Now pull up the blanket, over their toeses, 
Until all that sticks out is the tips of their noses."

(Follow the instructions. My, these children 
have big noses, too! Is it nice to tease? Of course not!)

"See how cleverly each corner locks.
Now, reach in and pull up, to open your box."

(Do I need to draw you a picture? This really is a very 
clever way to fold a box. To make a lid for your box, 
just take another sheet of paper, and repeat the story 
all over again, with two minor changes. Leave small gaps 
in the middle, "It is OK", when you make the folds which 
introduce the girls from next door. This will make the 
lid wider and longer than the box, but not quite as deep. 
Each lid has a folded rim, which can serve as a convenient 
label for the intended contents of each box. Just be careful 
to notice how the lid will fit on the box, so you don't 
write the label up-side-down!)

(Now that you have mastered this story, if you ever get paid 
for it, you will be a "professional boxer"! (A joke. Ha, ha.))

---- ----- ----- ----- ----- ----- ----- ----- ----- ----- 


Learn humility! Try to program a computer! Ray Calvin Baker (talk) 21:20, 9 August 2012 (UTC)

CORRECTIONS in progress! Ray Calvin Baker (talk) 21:05, 11 August 2012 (UTC)

	(other materials)

My apologies are in order. I had an incorrect diagram in this section. 
The old diagram is good for taping equilateral triangles together (see 
above) to make the regular icosahedron. but it is totally incorrect 
for making that shape with string and plastic straws. A complete 
rewrite of this section is in progress.

	75 Plastic soda straws (to make one ornament)
	white glue (optional)

	wire loop (narrow enough to fit through the hollow 
		straws. Instructions to make this tool are 
		given above.)
	Ball-point pen 
	Ruler (optional)


	WARNING! Pieces this size will make an enormous ornament
	nearly 1 meter in diameter! That's suitable if your Christmas 
	tree is a Giant Sequoia or a Giant California Redwood. But, 
	you may wish to cut eaqch piece in half, to make two smaller 
	ornaments instead.

	Place two straws side-by-side. Estimate the location 
	of the center of the straws, then make a short mark 
	there with the ball-point pen. Turn one of the straws 
	end-for-end, then place it back beside the other 
	marked straw. If the marks line up, you did a good 
	job of finding the center. If the marks are off 
	by a fraction of an inch, estimate the location of the 
	place midway between the short marks, then make a 
	longer mark there. (This process should reduce your 
	error by half.) OR, use the ruler to measure off half 
	the length of the straws. Cut both straws in half at the 
	marked 	places. Use these half straws to measure off the 
	halfway point on thirteen more straws. Mark and cut 
	those straws in half.

	Now you should have 30 half length pieces, and 60 
	full length pieces. 


CORRECTIONS (actually a complete rewrite of this section) are in progress. It's still not complete yet, and it needs pictures (this is a "how to" lesson).

Ray Calvin Baker (talk) 23:35, 15 August 2012 (UTC)

There are three kinds of people in the world: those who can count, and those who can't. -- One of Ian Stewart's mathematical jokes. (page 1, _Professor_Stewart's_Cabinet_of_Mathematical_Curiosities_, ISBN 978-0-465-01302-9)

                                                                 | DIAGRAMS:                                   |
                                                                 |                       (2)                   |
        Two general principles are important to keep in mind at  |       |             /  |  \       These are |
        all times while trying to build the core of this model.  |       |           /    |    \     SKETCHES, |
        (1) Exactly FIVE straws must meet at every vertex.       |  ----(1)----   (2)----(1)----(2)  not exact |
        (2) Every vertex must be surrounded by a ring of FIVE    |      / \         \    / \    /    scale     |
        straws in a pentagon shape.                              |     /   \         \  /    \ /     drawings! |
                                                                 |                    (2)----(2)               |
                                                                 | Principle 1       Principle 2               |
                                                                 |                                             |
                                                                 |         ( )                                 |
                                                                 |       /  |  \                               |
                                                                 |     /    |    \                             |
        As you approach the end of building the core, you will   | ( )-----( )-----( )                         |
        find that adding the last few straws will require that   |  |\     / \    / |     Severe distortion    |
        you observe both general principles at the same time.    |  | \   /   \  /  |     results from trying  |
        Some straws are simultaneously the fifth straw to be     |  |  ( )=====( )  |     to show a 3-D        |
        added to a vertex, and the fifth straw to make a         |  |  / \    /  \  |     structure on         |
        pentagon ring. Eventually, you will get to the last      |  | /   \  /    \ |     a flat surface!      |
        straw, which completes TWO vertices AND two pentagonal   | ( )-----( )-----( )                         |
	rings.                                                   |     \    |    /                             |
                                                                 |       \  |  /                               |
                                                                 |         ( )                                 |
                                                                 | The last straw (=====) does multiple duty.  |

        It takes thirty (30) pieces to make the central core. 
        I will list the numbers of the pieces involved at the 
        beginning of each paragraph of the following 

        Once you have made a few stars using this method, you 
        are free to use your own plans. However, there are many 
        ways to get stuck, or to miss tying a knot where one 
        belongs. Thus, I recommend that you stick with my 
        printed plan. Besides that, you may help me find and 
        eliminate mistakes (if there are any) if you follow a
        written plan consistently.

        NOW START: (1, 2, & 3) Push the wire loop down the 
        hollow middle of one of the short pieces (1). Thread one 
        end of the string through the wire loop, then pull the 
        wire (with the string) back out of the piece of 
        plastic straw. Repeat this process two more times, until 
        you have three pieces threaded onto the string (1, 2, & 3).

        Tie a knot in the string, then pull it tight (not TOO 
        tight, or you may split a plastic straw!) so that the 
        three plastic pieces (1, 2, & 3) outline an equilateral 
        triangle. Note: when I say, "tie a knot" while building 
        this model, I really mean, "Tie three or four knots". 
        No one wants a model that comes apart too easily. When 
        ln doubt, tie another knot!

	You should have something that looks like this. 
	(The dot indicates the location of the knot)

	   \      /    Pieces 1, 2, & 3.
            \    /
          (1)\  /(3)

	(4 & 5) Stretch out a length of string from the knot 
        (about the length of your arm should be fine.) You can 
        tie on more string any time, if you find that you need 
        more string. Just try to plan it so that your splices 
        will be hidden deep in the middle of a straw. Thread 
        two more pieces (4 & 5) of straw onto the string. Tie 
        another knot. Now you should have something like this.

	   \      /\       Pieces 4 & 5 added. 
         (1)\ (3)/  \(5)
             \  /    \

 	(6 & 7) Keep on threading short pieces of plastic straw and 
	tying knots until you have a network something like this.

              (2)     (6)
           ________A_______      Notice that there are FOUR 
           \      /\      /      straws at vertex A. 
            \ (3)/  \(5) /
          (1)\  /    \  /(7)
              \/______\/.        Pieces 6 & 7 added. 
                 (4)    )

        (8 & 9) Add two more pieces of plastic straw, until you 
        have a flat structure like this.

              (2)     (6)
           \      /\      /\
            \ (3)/  \(5) /  \(9)   Pieces 8 & 9 added. 
          (1)\  /    \  /(7) \ 
                  (4)  D  (8)

        (10 & 11) Keep in mind that there are already four  
       straws at point "A". My strategy is to add the fifth 
        straw there, as soon as possible. Add straw pieces 
        (10 & 11) as shown below. Your structure should still 
        lie flat on your work table.

                     /\           Pieces 10 & 11 added. 
                (11)/  \(10)
            (2)    / (6)\         Notice that we have five 
        B ______(./______\E       straws together now,
          \      /\A     /\       where point "A" had been. 
        (1)\ (3)/  \(5) /  \(9)   Also, 4 straws come together 
            \  /    \  /(7) \     at "D" and at "E".
                 (4) D   (8)

        Since we now have five straws coming together at one 
        vertex, it is time to tie a final knot in this piece of 
        string. Cut the string about 1/4 inch from the knot.
        If you cut the string too close to the knot, the knot 
        may come loose, and your model may fall apart.

        (12) Next, we start with a fresh piece of string. 
        Tie this new string to the corner at point "B", per 
        the diagram above. Thread plastic straw piece (12) 
        onto the string, then loop the string around the 
        corner at "C". Pull the string tight, so that no 
        excess of string is visible at either end of plastic 
        piece (12). This will cuase you model to pucker up 
        into the shape outlining a pentagonal pyramid. It 
        will no longer lie flat. I will need to switch from 
        the diagrams which have served until now, to use 
        pictures of the model. (Diagrams will be distorted 
        because the shape is now 3-D and cannot be well 
        displayed, except by pictures.)

        Note: Each picture will be drawn independently 
        of all other pictures. I do not expect that the 
        labels of the vertices will be consistent between 
        pictures. The labels will apply only to the 
        paragraph which explains how to build the core of  
        the ornament, up to the stage shown in the picture.  
        (Perhaps I should try extra hard to make the labels 
        consistent throughout all of the pictures.)

|             (B)                Vertex B actually lies | 
|          //  || \\             behind vertex A;       | 
|     (1)//    ||   \\(12)       I lies behind F;       |
|      //   (2)||     \\         K lies behind D; and   | 
|    //  (3)   ||  (11) \\ .)    L lies behind E.       | 
| (G)=========(A)=========(C)    Actually, A and F      |
|  |\\       // \\       //|     should be farther      | 
|  | \\  (5)//   \\(6)  // |     apart.                 | 
|  (4)\\  //       \\  //(10)    B and I should be      | 
|  |   \\//   (7)   \\//   |     closer together.       |
|  |  K (D)=========(E) L  |     Severe distortion      | 
|  |   /  \\       // \    |     results from trying    | 
|  |  /    \\     //   \   |     to show a 3-D          | 
|  | /   (8)\\   //(9)  \  |     structure on           | 
|  |/        \\ //       \ |     a flat surface!        | 
| (J)---------(F)---------(H)    Vertex A has 5 straws; |
|    \         |         /       B has 3; C has 3;      | 
|      \       |       /         D has 4; E has 4;      |
|        \     |     /           F has 2; G has 3.      |
|          \   |   /             H, I, J, K, and L      |
|             (I)                have 0 straws.         |

Maybe I can use this diagram after all, to plan the pictures. 
I am the only person who needs to see it, and I understand 
the nature of the distortions, and can compensate. 
However, it may be good for my pupils to learn how to 
interpret diagrams, and to understand how they compare 
with pictures, so I'll leave the diagram in place. -- RCB
Double lines in the diagram indicate straws already in place.
Twelve straws in place

EXPLANATION OF THE COLOR-CODED PICTURE: Five straws around corner "A" are shown in black. Straws (1), (4), (7), and (10) are shown in orange. The last straw to be installed, (12), is shown in red. These five straws form a pentagonal ring around corner "A". Corner "A" is higher above the gray tabletop than the pentagonal ring. A string hangs loose from corner "C". We will use this string later, if it is long enough. If it is not long enough, we will splice on more string. A loop of two straws, (8) and (9), shown in yellow-orange, hangs below the model, from edge "D" -- "E".

        (13 & 14) So, tie a string to the corner at D.
        Put two plastic pieces (13 & 14) onto the string.
        Loop the string around corner F, then pull it 
        tight. Tie a knot at F.

Then we have this: 
|             (B)                Vertex B actually lies | 
|          //  || \\             behind vertex A;       | 
|     (1)//    ||   \\(12)       I lies behind F;       |
|      //   (2)||     \\         K lies behind D; and   | 
|    //  (3)   ||  (11) \\ .)    L lies behind E.       | 
| (G)=========(A)=========(C)    Actually, A and F      |
|  |\\       // \\       //|     should be farther      | 
|  | \\  (5)//   \\(6)  // |     apart.                 | 
|  (4)\\  //       \\  //(10)    B and I should be      | 
|  |   \\//   (7)   \\//   |     closer together.       |
|  |  K (D)=========(E) L  |     Severe distortion      | 
|  |   // \\       // \    |     results from trying    | 
| (13)//   \\     //   \   |     to show a 3-D          | 
|  | //  (8)\\   //(9)  \  |     structure on           | 
|  |//  (14) \\ //       \ |     a flat surface!        | 
| (J)=========(F)---------(H)    Vertex A has 5 straws; |
|    \         |         /       B has 3; C has 3;      | 
|      \       |       /         D has 5; E has 4;      |
|        \     |     /           F has 3; G has 3.      | 
|          \   |   /             H, I, K, and L         | 
|             (I)                have 0 straws.         | 
|                                J has 2 straws.        |

[I need another picture—13 & 14—here. It may be from a slightly different vantage point. This picture should be based upon a projection of an icosahedron. -- RCB]

        (15 & 16) Put two more plastic pieces onto the 
        string, then tie a knot at E. Since you have tied 
        the fifth plastic piece at E, you may cut and trim 
        the string.

Then we have this: 
|             (B)                Vertex B actually lies | 
|          //  || \\             behind vertex A;       | 
|     (1)//    ||   \\(12)       I lies behind F;       |
|      //   (2)||     \\         K lies behind D; and   | 
|    //  (3)   ||  (11) \\ .)    L lies behind E.       | 
| (G)=========(A)=========(C)    Actually, A and F      |
|  |\\       // \\       //|     should be farther      | 
|  | \\  (5)//   \\(6)  // |     apart.                 | 
|  (4)\\  //       \\  //(10)    B and I should be      | 
|  |   \\//   (7)   \\//   |     closer together.       |
|  |  K (D)=========(E) L  |     Severe distortion      | 
|  |   // \\       // \\   |     results from trying    | 
| (13)//   \\     //   \\(16)    to show a 3-D          | 
|  | //  (8)\\   //(9)  \\ |     structure on           | 
|  |//  (14) \\ //  (15) \\|     a flat surface!        | 
| (J)=========(F)=========(H)    Vertex A has 5 straws; |
|    \         |         /       B has 3; C has 3;      | 
|      \       |       /         D has 5; E has 5;      |
|        \     |     /           F has 4; G has 3.      | 
|          \   |   /             I, K, and L            | 
|             (I)                have 0 straws.         | 
|                                J and H have 2 straws. |

[Third picture—15 & 16—goes here.]

        (17) Use the string hanging from corner C. Put a 
        piece of plastic straw (17) onto the string. Loop 
        the string about corner H, then pull it tight so 
        there is no excess string showing at either end of 
        piece (17). This should cause your model to "pucker 
        up" around corner E, in a way similar to the way 
        the model puckered when you completed the ring 
        around corner A, earlier. CAUTION! You have just 
        formed a second pentagonal ring, around corner E! 
        Be sure that both corners, A and E, will end up at 
        the same distance from the place where the center 
        of your ornament will be, eventually. You do not 
        want any part of your central core to be "inside 

After the second ring has formed, around corner E, we have this: 
|             (B)                     Vertex B actually lies | 
|          //  || \\                  behind vertex A;       | 
|     (1)//    ||   \\(12)            I lies behind F;       |
|      //   (2)||     \\              K lies behind D; and   | 
|    //  (3)   ||  (11) \\            L lies behind E.       | 
| (G)=========(A)=========(C)         Actually, A and F      |
|  |\\       // \\       //||         should be farther      | 
|  | \\  (5)//   \\(6)  // ||         apart.                 | 
|  (4)\\  //       \\  //(10)         B and I should be      | 
|  |   \\//   (7)   \\//   ||         closer together.       |
|  |  K (D)=========(E) L  ||(17)     Severe distortion      | 
|  |   // \\       // \\   ||         results from trying    | 
| (13)//   \\     //   \\(16)         to show a 3-D          | 
|  | //  (8)\\   //(9)  \\ ||         structure on           | 
|  |//  (14) \\ //  (15) \\||         a flat surface!        | 
| (J)=========(F)=========(H)         Vertex A has 5 straws; |
|    \         |         /  (         B has 3; C has 4;      | 
|      \       |       /     )        D has 5; E has 5;      |
|        \     |     /                F has 4; G has 3.      | 
|          \   |   /                  H has 3. I, K, and L   | 
|             (I)                     have 0 straws.         | 
|                                     H has 3, and J has 2.  |

[Fourth picture—17 -- goes here. -- RCB]

        (18 & 19) These complete 5 straws at F.

[Fifth picture—18 & 19—goes here. -- RCB]

Essential error-correcting rewrite still in progress. Pictures may have to wait a while. I need to create them, then upload them to Wikimedia Commons.

Ray Calvin Baker (talk) 23:35, 15 August 2012 (UTC)

End section 20.


Limit(anything) as time approaches infinity AND a programmer keeps trying = PERFECTION! Hopefully, that's worth waiting for. Ray Calvin Baker (talk) 21:35, 9 August 2012 (UTC)

	The core has 20 equilateral triangles. Our next task is 
	to tie three full-length straws above the three corners 
	of each of these equilateral triangles. This should be 
	a fairly obvious matter of adding straws and tying knots. 
	I think the easiest to manage this in a systematic 
	fashion is this. Work on one triangle at a time. 
	(1) Take a piece of string about three times as long as 
	a straw. 
	(2) Tie one end of the piece of string to one of the 
	corners of the triangle you have elected to work on. 
	(3) Thread two full-length straws onto this string. 
	(4) Tie the loose end of the string to a second corner 
	of the triangle you are working on. 
	(5) Take another piece of string almost twice the 
	length of a straw. 
	(6) Tie one end to the third corner of the triangle 
	you are working on. 
	(7) Thread a full-length straw onto this string. 
	(8) Tie the loose end to the joint between the first 
	two straws you added in steps 2, 3 and 4. This should 
	position a rigid point above one of the 20 triangles 
	of the core of the ornament.

	Repeat this process for each of the remaining 19 


Seven or eight more to go! Then I can start working on the SERIOUS problems! Ray Calvin Baker (talk) 21:38, 9 August 2012 (UTC)

	You will probably wish to trim loose ends of string, or 
	tuck them out of sight. You may wish to leave a large 
	loop for hanging your ornament. A few drops of white 
	glue may help secure the knots and keep loose ends out 
	of the way.

	When you make your next star, see how many ways you can 
	figure out to save string, and make the tying of the 
	knots a more efficient process. I tried to keep things 
	as easy as possible for you, while we worked on your 
	first star.

---- ----- ----- ----- ----- ----- ----- ----- ----- ----- 

23. KEPLER'S STAR edit

Don't lose your sense of humor. You're gonna need it! Ray Calvin Baker (talk) 21:40, 9 August 2012 (UTC)

	(Compare with M. C. Escher's "Two Worlds".) 
	(Paper sculpture using business cards)

	12 cards or thick paper 2 inches by 3+1/2 inches 
		(Instructions for cutting these cards are 
		given above.)
	white glue or glue sticks (technically optional, 
		but highly recommended, especially for 




Many who have published designs for modular origami have done 
a great job of describing how to make the modules, but (except 
for a few hints) have left it up to the folder how to assemble 
those modules into complicated final models. This is understandable, 
if one is discouraged by the large number of detailed diagrams 
which would be required for a large, complex design.

I may be the first to completely document this phase of the
construction, if I can persuade my computer to make the necessary 
diagrams. -- RCB

---- ----- ----- ----- ----- ----- ----- ----- ----- ----- 


Every problem you encounter is really an opportunity to improve this world, in a clever disguise. Ray Calvin Baker (talk) 21:43, 9 August 2012 (UTC)

	V. THE HOPPING BUNNY (quick, easy origami toy, with 
	a story: "The Lonely Little Japanese Lady")

3 inch by 5 inch index card

(Follow along with the story; adapted from the video, 
"A Peace of Paper".)

	"The Lonely Little Japanese Lady"

[ INCOMPLETE #17 of 23 -- RCB ] This story also may benefit with pictures.

"Once upon a time there was a Japanese Lady, who would wake 
up every morning and begin her exercises. She lived by herself, 
and was lonely, so she was always hoping for company."

(Display a 3 by 5 index card, which represents the Japanese 

"She stretched out her right arm, then bent over and touched 
her left knee. Then she stood up straight again."

(Bend the top right corner of the card, so that what was the 
top edge lies over the left edge of the card. Crease, then 
unfold the card.)

"Then, she stretched out her left arm, bent over, and touched 
her right knee. Then she stood up straight again."

(Bend the top left corner of the card, so that what was the 
top edge lies over the right edge of the card. Crease, then 
unfold the card.)

"After many years of doing these stretching exercises every 
morning, she was so flexible that she could stretch out both 
arms, bend over backwards, and touch the backs of both knees. 
Then she stood up straight again."

(Don't you try this at home on yourself! You are not a three 
by five index card! But fold the card backward so that the 
corners, which were on top, lay on the creases left by the 
first two folds.)

"Would you like to see the little house the lonely Japanese Lady 
lives in? Just walk up to her door. There in the middle of the 
door, where the lines cross, is the doorbell button. Press the 
button to ring the doorbell, then pull the roof down into 
place to see the house."

(Hold the card up, with the top bent back slightly away from 
you. This represents the door, with lines that cross in the 
middle. Press the doorbell button. The two sides of the card 
should snap toward you. Pull the roof down into position, and 
look at the little house.)

"Now, imagine that the little Japanese Lady has come to the 
door. She feels that it is rather chilly outside today, so she 
wraps her shawl about herself. 'Would you like to come inside 
to warm up?', she asks. 'I'm sorry. I have other things I must 
do today, so I must be on my way. Perhaps you will have another 
visitor today.', you reply."

(Pull both vertical edges of the "house" forward, so that these 
edges of the card meet in the middle. Crease the new folds 

"The little Japanese lady still feels chilly, so she claps her 
hands together in front of her, several times."

(Pull the two triangular flaps, which represent her arms, 
forward several times, as if she's clapping her hands.)

"Thinking she is a bit stiff from the chill, she repeats one of 
her stretching exercises. She bends backward so far that the 
top of her pointed hat touches the bottom of her heels."

(Bend the pointed top of the card back until it touches the 
bottom of the card, in the middle.)

"Thinking that more vigorous excercise may help her warm up, 
she leaps into the air, and kicks out both her feet so far 
that her toes touch her tummy. She lands quickly and 
gracefully on her feet."

(Bend the bottom of the folded card forward, so that the lowest 
edge meets the crease which marks the lady's waist. Fold the 
card into a compact shape, to suggest how she lands quickly 
and gracefully.)

"When the Japanese Lady turns around again, she sees that, 
indeed, she does have another visitor today. There, on the 
doorstep, she sees a little bunny. She leans down to pet the 
bunny, but it hops away."

(In its compact shape, the folded card resembles a rabbit, 
with big ears. If you stroke your finger down its back, the 
bunny may hop for you!)

"'Perhaps I will see him again tomorrow', the Lady says to 
herself. Indeed, she will, if you take another three by five 
index card, and share this story with someone tomorrow."

---- ----- ----- ----- ----- ----- ----- ----- ----- ----- 


The real reason I am such a klutz is this: to give YOU an opportunity to do SO MUCH BETTER! Ray Calvin Baker (talk) 21:47, 9 August 2012 (UTC)

	(a starry paper sculpture 
	from ordinary sheets of paper)


---- ----- ----- ----- ----- ----- ----- ----- ----- ----- 


Close, but NO CIGAR! Ray Calvin Baker (talk) 21:50, 9 August 2012 (UTC)


	(I may be among the first to completely document 
	this important phase of the construction.) 3

[ INCOMPLETE! #19 of 23 -- RCB ] but I have an old file, in which I began to 
describe this project. -- RCB ]

---- ----- ----- ----- ----- ----- ----- ----- ----- ----- 


Closer, but still NO CIGAR! Ray Calvin Baker (talk) 21:52, 9 August 2012 (UTC)

	(Compare with M. C. Escher's prints, "Gravitation" 
	and "Order and Chaos".)
	(The beauty of modular origami is that the same 
	module can be assembled in several, completely 
	different ways. Learn to fold just one module; 
	but be able to learn how to make several 
	different models using that module.)

[ INCOMPLETE! #20 of 23 -- RCB ] 1st STELLATION

---- ----- ----- ----- ----- ----- ----- ----- ----- ----- 


Ray Calvin Baker (talk) 21:54, 9 August 2012 (UTC)

	IX. A SIMPLE JUMPING FROG (origami toy)


---- ----- ----- ----- ----- ----- ----- ----- ----- ----- 

Coming ASAP—an INCOMPLETE ROUGH DRAFT! I am working on a poster for traditional classroom use. I hope this will help me make good illustrations for Wikimedia Commons, which I can reference within this topic. Ray Calvin Baker (discusscontribs) 14:46, 4 September 2013 (UTC)

This is my "E:/WikiversityStuff/Paper&Prep_1.txt" file, 
created FRI 2013 AUG 26 11:20 AM, 
revised SUN 2013 SEP 08 10:46 AM.


Origami paper is very good for use in origami, but it is expensive, 
and not often available in the large sizes which beginners will find 
most useful. It is usually white on one side, and brightly colored 
on the other side.

When I was a professional computer programmer, I usually had access 
to huge boxes of slightly used computer paper. It was thin, flexible, 
and precisely cut to go flawlessly through high-speed printers. 
Also, it came in LARGE 11 inch by 14 inch sheets.

Now that I have retired, I usually use 8 + 1/2 inch by 11 inch 
copy machine paper. It is widely available from office supply stores, 
prepackaged in reams of 500 sheets, for a price usually less than 
$7 per ream. (Sometimes white paper is available on sale for less 
than $5 per ream.) It comes in a wide range of beautiful colors 
(mostly pastel colors), and is frequently available in several 

The thickness of the paper is important, as it affects the 
flexibility and folding characteristics of the paper. I usually 
use what is called "20 pound" paper. This is the usual stuff 
one would use in a copy machine. Some of the brighter, bold colors 
come only in the "24 pound" thickness, which is somewhat stiffer. 
Card stock is usually available (but more expensive). It is very 
nice for greeting cards and some types of paper sculpture. 
I have even used poster board (NOT the foam-filled kind) for 
making large free-standing angels, and Christmas tree ornaments.

I recommend that you experiment with every kind of paper you can 
find, to experience as wide a range of folding characteristics as 
possible. Magazine pages, (glossy and not glossy), newspaper pages, 
brown paper from shopping bags and from wrapping paper rolls, 
even paper towels, have their uses for various models. The only 
types of papers I have not had success with are lotion-soaked 
tissues, and paper napkins. (Paper place mats are sometimes 
amusing to fold in restaurants.)

Additional topics:
Gift-wrap paper
Foil-laminated paper
Using paper from ROLLS

A section on "Preparing Paper" should follow this section, 
but it is still INCOMPLETE.

The end of the "E:/WikiversityStuff/Paper&Prep_1.txt" file.

Ray Calvin Baker (discusscontribs) 15:23, 8 September 2013 (UTC)

This is my "E:/WikiversityStuff/ FrogFolding_1.txt" file, which was 
created WED 2013 AUG 28 03:56 PM, 
revised SUN 2013 SEP 08 10:58 AM. 
#1 -- Hop 1 through Hop 10

Ray Calvin Baker (discusscontribs) 19:46, 25 September 2013 (UTC)

actual size.

Why do I make most of my pictures at 1/2 scale? So I don't waste 
space on the posters or in the pictures! The initial folds for 
most models require showing the entire piece of paper, and there 
are no small details until later. Later, (see NOTE 16) , when the 
folded paper model is more compact, and small details will be 
important, I will again make my illustrations in their full 
actual size.

HOP 3 (GRAY COLOR). Observe the starting square, shown at 1/2
scale. I don't want you to be confused -- I have merely drawn the 
starting square a second time, at the smaller scale.

Sometimes in origami books, just part of a model will be drawn, so 
as to show how to develop details, without redrawing parts of the  
entire model which have not changed. Changes of scale are also 
common in origami books, for the reasons I have already mentioned.


Now I would like to introduce Randlett-Yoshizawa notation. On the 
model for HOP 5, The dashed line from corner "B" to corner "D" 
indicates a "valley fold". (In my computer drawings, I usually show 
valley folds as GREEN lines -- think, "lush GREEN valleys. GREEN 
lines are easier for me to draw on my computer than dashed lines.) 
The back-and-forth arrow indicates, "Fold, Crease, then Unfold".

To make a "valley fold", lift an edge, a corner, or some other part 
of your model, move it over, then press it down against some other 
part of your model. For example, to get to HOP 7, you must move 
corner "A" and press it down against corner "C". These are the 
"anchor points" for this fold -- they help you position the fold 
very precisely.

The "anchor points" are points between which you expect to form 
a fold or crease. Usually, but not always, you will want a sharp 
crease, because a sharp crease does allow the paper to fold as if 
it had a hinge. I generally sharpen a fold into a sharp crease by 
running my thumb nail along the fold.

Origami books usually show you where the folds belong, but they 
don't always show you the "anchor points", which define the fold 
which is supposed to form midway between them. You must learn to 
figure out for yourself where the "anchor points" for each fold 
belong. When you have identified the "anchor points" correctly, 
making the fold is usually much easier.

The way origami folds are usually drawn in books might suggest to 
you that the paper folds like a hinge. But, it does NOT work that 
way at all (until and unless you have made a sharp crease)! HOP 6 
is intended to show you that the paper tends to bend into a 
cylinder or cone shape, somewhat like a stylized teardrop shape. 
Actually, the flexibility of the paper in that cylinder or cone 
shape allows you to position the "anchor points" of your fold 
quite accurately.

Some complicated models described in origami books require a lot 
of "prefolding". You will fold and crease and unfold for many 
steps, and it may not seem that you are accomplishing anything, 
because you unfold so much. But, in a later step, many of the 
creases you have formed will act as hinges, and large portions 
of the model will be shaped by those hinges.

At other times, you will fold, crease and unfold, just to form a 
crease line. Sometimes, crease lines are used as "construction 
lines". They are not part of the final model, but they act as 
guide lines, to help you construct other folds more easily.

Origami is not about strength, or using brute force to coerce the 
paper. Such force may tear the paper, spoiling your model. Rather, 
origami is more about using gentle coaxing to persuade the paper 
to drift into the position you desire. So, never rush, or allow 
yourself to be rushed. You need accuracy, not speed!

Here is a secret that may help you position your folds exactly. 
Once you have established the "anchor points" for your fold, 
and bent the paper so that one anchor point lies on top of the 
other, hold the paper down with one finger. Be very careful that 
you do not allow those held-down anchor points to be moved. Hold 
them securely with the fingers of one hand. Then, slide one finger 
on your other hand from a place near the "anchor points" to a 
place near the middle of your intended fold. This will tend to 
flatten the paper cylinder, and start your fold in its middle. 
Then, gently brush the paper from where the fold has started to 
one of the places where the fold ends. Brush the other half of 
the fold in a similar way. Now, when you move a finger along the 
newly formed fold, you should feel it squash into exact position. 
You may need to try these moves several times until they work 
well for you. Be gentle!

HOP 5 (RED COLOR). Observe the GREEN dashed line. This shows you 
where to make a valley fold. Observe the back-and-forth arrow. 
This tells you, "Fold, crease, then unfold".

The letters, "A", "B", "C", and "D", are intended to help you 
identify the four corners throughout the next few "hops".

HOP 6 (RED-ORANGE COLOR). Observe that the paper tends to form a 
cylinder. It will not act like a hinge here until you have made 
a sharp crease here.

HOP 7 (LIGHT ORANGE COLOR). Flatten the cylinder, as suggested in 
NOTE 4. Congratulations! You have made your first valley fold!

Crease the fold sharply, then unfold it, leaving only the crease 

On the poster, corners "B", "C", and "D" are glued to the poster 
board. Corner "A" tends to lie slightly away from the poster board, 
because of the valley fold in the paper.

HOP 8 (YELLOW-ORANGE COLOR) Observe a second dashed line, this 
time from corner "A" to corner "C". For this fold, your 
"anchor points" will be established by placing corner "B" on top 
of corner "D". Again, the back-and-forth arrow tells you, 
"Fold, crease, then unfold".


It is rather wasteful of space on the poster or in the drawings for 
one "HOP" to show the results of a fold, and for the next "HOP" to 
show the notation for the next fold. So, from now on, wherever it 
seems practical, I will show the results of one fold, and the 
notation for the next fold, all on the same drawing.

HOP 10 (LIGHT GREEN COLOR). Observe the results of the first two valley 
folds. They intersect in the middle of the paper square.

#2 -- Hop 11 through Hop 17

Ray Calvin Baker (discusscontribs) 20:29, 25 September 2013 (UTC)

SPECIAL INSTRUCTION 11 (PINK COLOR). Turn the model over. The easiest 
way to do this, is to let the left edge of your model remain on the 
table, as if there were a hinge there. Then lift the right edge of 
your model, push it towards the left, then let it drop back onto 
the table. Yes, there are several different ways to turn a model 
over. Each different way may leave your model with a different 
orientation, so always look ahead at least one diagram to see 
exactly how you should turn your model over.

HOP 12 (TEAL COLOR). Observe the other side of your 
partially-folded model. Observe that the folds which formerly 
looked like valleys now look like mountain ridges. Folds like 
these are called "mountain folds", and are usually shown in 
origami books as "dash dot" lines. I usually draw them as 
purple lines in my computer drawings. Think, "Purple mountain 

"Lush green valley" or "Purple mountain majesty"? It's always just 
the same fold, depending only on the direction from which you view 
it. And this is really all there is to origami -- valley folds and 
mountain folds -- although sometimes you will form a cluster of 
folds, all at the same time. You will see this happen when you lift 
a cheek of your frog model and form an eye, all at the same time, 
as in hops 36, 37, and 38.

HOP 13 (LIGHT BLUE COLOR). Observe the dashed line which runs 
parallel to the top edge of the model. This is sometimes called 
a "book fold", because it leaves edges of your model parallel, 
like the edges of the pages in a book are parallel.


Take your model up off the table with one 
hand. Gently press up, in the center of the model where three creases 
intersect, using a finger on your other hand. The model should snap 
into another configuration.

HOP 15 (LIGHT VIOLET COLOR). Observe that the model has started to 
take up the shape of an isoceles right triangle (It was a square 
before). Help your model take up that shape.

It may bulge a little bit. Try to press it flat. (Try to get 
the middle to lie flat first, then crease the edges again) You 
may need to let some of the creases shift slightly.


As promised earlier, in NOTE 2, I am going 
to resume making my models and drawings full actual size.

HOP 17 (WHITE ON YELLOW). Observe the final result of part one. It 
resembles an upside-down basket. Turn it around, and it will 
hold water, at least until the paper gets soggy. This is called, 
"the Water Bomb Base", because it is an early stage of folding the 
traditional Japanese Water Bomb. It is called a Base because it is 
also an early stage of folding many other models.

The end of the "E:/WikiversityStuff/ FrogFolding1.txt_" file. 

Ray Calvin Baker (discusscontribs) 15:28, 8 September 2013 (UTC)

This is my "E:/WikiversityStuff/ FrogFolding_2.txt" file, which was 
created SUN 2013 SEP 08 11:13 AM, 
revised SUN 2013 SEP 08 11:13 AM.



#3 -- Hop 18 through Hop 22

Ray Calvin Baker (discusscontribs) 20:29, 25 September 2013 (UTC)

HOP 18 (WHITE ON YELLOW). Part two starts with the "Water Bomb Base", 
which you completed in part one. Observe that I have added a dashed 
line, to indicate where to start folding the frog's left front leg.

Observe that this time, the arrow is NOT a back-and-forth arrow. 
This time, the arrow means, "Fold, Crease, and Leave the paper 

HOP 19 (GRAY COLOR). Observe that the left front leg has been started. 
Observe the dashed line, which tells you where to start folding the 
right front leg.

HOP 20 (RED COLOR). Observe that both front legs have been started. 
I hope you have made your frog symmetrical!

SPECIAL INSTRUCTION 21 (PINK COLOR). Turn the model over.

HOP 22 (RED-ORANGE COLOR). Observe the frog's back. His front feet 
will be formed underneath his head.

#4 -- Hop 23 through Hop 28

Ray Calvin Baker (discusscontribs) 20:29, 25 September 2013 (UTC)


Until now, you have had well-defined anchor points to guide your folds -- 
corners, edges, or previous creases. But to fold the frog's left 
hind leg, you need to estimate the position of the fold. Too 
narrow, and your frog will look weak. Too wide, and your frog 
may not hop at all. Making folds like this takes experience and 
good judgement. So look carefully at the model I have provided,  
and try to fold your frog so that it looks like mine.




SPECIAL INSTRUCTION 27 (PINK COLOR). Turn the model over.


#5 -- Hop 29 through Hop 34

Ray Calvin Baker (discusscontribs) 20:29, 25 September 2013 (UTC)







#6 -- Hop 35 through Hop 39

Ray Calvin Baker (discusscontribs) 20:29, 25 September 2013 (UTC)

SPECIAL INSTRUCTION 35 (PINK COLOR). Turn the model over.

HOP 36 (DARK VIOLET COLOR). Observe how the frog's "cheeks" 
protrude slightly from underneath his head. This is a tricky 
fold which wraps the "cheek" around the edge of the frog's 
head, and simultaneously forms one of the frog's bulging eyes.


HOP 38 (YELLOW-GREEN COLOR). At last! The completed frog! 
This frog is glued to the poster board, to keep the set of 
instructions complete, so that other people can fold frogs, 
too. But the simple hopping frog is not much fun until it 
starts hopping.

NOTE 39 (WHITE ON YELLOW) How to make your frog hop. Put 
the frog on a firm surface. Then, put a finger on top of 
the frog's back, and press down. You should feel some 
"springiness" in your frog as you compress him. Then slowly 
slide your finger away from the frog's nose. He should hop 

HOP 40 (DARK GREEN ON YELLOW). This completed frog is 
attached to the poster only by a paper clip, so that you may 
remove it and try him out. Please do not lose the frog or the 
paper clip. Please re-attach the frog, using the paper clip, 
when you are done playing with him, so that other people may 
enjoy him, too -- at least, until they learn how to fold a 
simple hopping frog, too!.

Here is a local Eastern Shore Maryland joke. (It won't make 
sense elsewhere.) "Remember, frogs cost less in Preston!"

The end of the "E:/WikiversityStuff/ FrogFolding_2.txt" file. 

Ray Calvin Baker (discusscontribs) 15:30, 8 September 2013 (UTC)

29. ANGEL edit

Only ONE MORE to go~ Ray Calvin Baker (talk) 21:55, 9 August 2012 (UTC)

	X. ANGEL (a simplified origami ornament or finger puppet)

[ INCOMPLETE!#22 of 23  -- RCB ] ANGEL

---- ----- ----- ----- ----- ----- ----- ----- ----- ----- 


Thank you for your patience. :-) Next time, I get to begin more work on the SERIOUS problems. Ray Calvin Baker (talk) 21:57, 9 August 2012 (UTC)

	(authentic traditional Japanese origami)


The end.