The pairs of matrices shown in the following boxes are twins. This is shorthand for the fact, that their rows are Zhegalkin twins. (Compare Zhegalkin matrix.)
Some of them are unusual, and have unusual names: SAND (a.k.a. minimal negation operator) could be called all but one.
Its reflection SNOR could be called no but one.
The name XOR is used for the parity function.
The reflection of not XOR is called XAND. (Because the reflection of not OR is AND.) GAND is SAND extended by AND.
Its reflection GNOR is SNOR extended by not OR.
In ESAND and OSAND this extension happens only for an even or odd number of arguments. Their reflections are ESNOR and OSNOR. EQ makes sense as generalization of the biconditional, and is true if all arguments have the same truth value (but not if there are no arguments).
Each of these triangles is symmetric to another one (in two cases to itself). Only the triangle rows are symmetric (not the matrix rows).
Pairs with symmetric triangles are in the same box, e.g.:
XOR / OSAND,
SNOR / OSNOR
This section also shows pairs of matrices whose rows are Zhegalkin twins.
The binary patterns are the same as in the lower triangular matrices in the section before, but they are horizontally and vertically flipped.
Just like in the section before, there are pairs of matrices whose triangle rows are horizontally mirrored. Here they are marked with the same color.
The labels in this section are to be understood like this:
Take the lower triangular twin with that label, flip it horizontally and vertically, and make the twin of that.
E.g. take the XOR twin from the last section.
Flip it to get not XAND in this section. The twin of that is XOR in this section. (Half of these rows are noble, i.e. their own twins.)