Correct.muzik wrote: October 27th, 2025, 9:08 pm In 4D, the eight cell-adjacent cells once again just return the same tesseract honeycomb. I assume the 24 face-adjacent cells result in the 24-cell tiling?
The 32 edge-adjacent cells give the original tesseract honeycomb.muzik wrote: October 27th, 2025, 9:08 pm What do the 32 edge-adjacent cells and 16 vertex-adjacent cells result in?
The 16 vertex-adjacent cells give the 24-cell tiling rotated and scaled by sqrt(2), possibly with a non-totalistic rule.
For higher dimensions n. The 2^k*(n choose k) cells that are k-adjacent give you the standard grid lattice if k<n is odd, the Dn root lattice if k<n is even, and the dual root lattice Dn* if k=n.