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Bn Em wrote on Mon, Mar 25 04:39 PM UTC in reply to Niels van Ham from 09:23 AM:

4D has at least two more symmetrical tilings: Xyrixa‐prism (a line of boards each of which has the same topology as Tetrahedral Chess or OctHex), as well as one that continues the Hex–Xyrixa–??? line which I've wondered about for a while but have never looked into in enough detail. There might also be one or two more in the class of the following.

There is also one more 3D one that Charles never explored (and noöne else seems to have used either), the bitruncated cubic honeycomb. Which corresponds to the other close‐packing of spheres that the Xyrixa geometry doesn't cover.

Unfortunately Charles hasn't been seen here since 2016, so even if he were interested in 4D (which he stated several times that he wasn't) it's unlikely that he'll do much on that front. And even there, the Hybrid Diagonal stuff is already kind of pushed into more‐or‐less expansion article territory.

If you're really interested, of course, you can devise some names yourself :‌)


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