Template:Regular convex 4-polytopes

Sequence of 6 regular convex 4-polytopes
Symmetry group A4 B4 F4 H4
Name 5-cell

Hyper-tetrahedron
5-point

16-cell

Hyper-octahedron
8-point

8-cell

Hyper-cube
16-point

24-cell

Hyper-cuboctahedron
24-point

600-cell

Hyper-icosahedron
120-point

120-cell

Hyper-dodecahedron
600-point

Schlรคfli symbol {3, 3, 3} {3, 3, 4} {4, 3, 3} {3, 4, 3} {3, 3, 5} {5, 3, 3}
Coxeter mirrors
Mirror dihedrals ๐…/3 ๐…/3 ๐…/3 ๐…/2 ๐…/2 ๐…/2 ๐…/3 ๐…/3 ๐…/4 ๐…/2 ๐…/2 ๐…/2 ๐…/4 ๐…/3 ๐…/3 ๐…/2 ๐…/2 ๐…/2 ๐…/3 ๐…/4 ๐…/3 ๐…/2 ๐…/2 ๐…/2 ๐…/3 ๐…/3 ๐…/5 ๐…/2 ๐…/2 ๐…/2 ๐…/5 ๐…/3 ๐…/3 ๐…/2 ๐…/2 ๐…/2
Graph
Vertices[a] 5 tetrahedral 8 octahedral 16 tetrahedral 24 cubical 120 icosahedral 600 tetrahedral
Edges 10 triangular 24 square 32 triangular 96 triangular 720 pentagonal 1200 triangular
Faces 10 triangles 32 triangles 24 squares 96 triangles 1200 triangles 720 pentagons
Cells 5 {3, 3} 16 {3, 3} 8 {4, 3} 24 {3, 4} 600 {3, 3} 120 {5, 3}
Tori 5 {3, 3} 8 {3, 3} x 2 4 {4, 3} x 2 6 {3, 4} x 4 30 {3, 3} x 20 10 {5, 3} x 12
Inscribed 120 in 120-cell 675 in 120-cell 2 16-cells 3 8-cells 25 24-cells 10 600-cells
Great polygons 2 squares x 3[b] 4 rectangles x 4 4 hexagons x 4 12 decagons x 6 100 irregular hexagons x 4
Petrie polygons 1 pentagon x 2 1 octagon x 3 2 octagons x 4 2 dodecagons x 4 4 30-gons x 6 20 30-gons x 4
Long radius
Edge length[c]
Short radius
Area
Volume
4-Content



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