Category:Hexadecachoric group; subgroups
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The symmetry groups currently in this category are those of tesseracts with binarily colored vertices, i.e. of 4-ary Boolean functions.
An n-ary Boolean function is represented as a vector of length 2n, but best understood as a period that repeats this pattern infinitely.
The symmetry of a Boolean function is the set of hypercube permutations that leave it unchanged.
Such a set is infinite, and has a pattern that can be described as periodic.
So e.g. the Boolean function x0 = (0, 1, 0, 1...) has one symmetry, which
- for arity 1 is represented by 1 permutation in a 2×1 matrix,
- for arity 2 is represented by 2 permutation in a 4×2 matrix,
- for arity 3 is represented by 8 permutations in an 8×6 matrix and
- for arity 4 is represented by 48 permutations in a 16×24 matrix.
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Subcategories
This category has only the following subcategory.