♫ Mirrors on the Ceiling . . .
♫ Pink Champagne on Ice . . .

The natural symmetry group of the 16 vertices of a tesseract
is generated by arbitrary permutations of parallel faces and
is of order 322,560.
(This is an abstract version of the Cullinane diamond theorem.)
For the corresponding cube theorem, see Cube Space.
Some backstory . . .
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