polychoronlover wrote:x4/3x4x3/2x3*a *a~c *b4d
wait, this one contains x3/2x and is degenerate. Not sure what you meant to write here...
When I saw this, I first thought of digging up my old papers from 2015 that first described these, but then I realized that I would probably be doing a more exhaustive search soon, so there wasn't really any need. But before I completed that search I suddenly remembered that one of the first uniform honeycombs I discovered after making my list had the symbol x4x~x4x3*a4/3*c *b4/3*d. It may well be that this is the one I originally wrote down, but I didn't notice that it was in a different family from the second-to-last one when I put it online (both have tetrahedral diagrams).
So I guess that my plan should have x4/3x4x3/2x3*a *a~c *b4d replaced with x4x~x4x3*a4/3*c *b4/3*d. I also missed x4o3/2x~x3*b, a member of the skivcadach regiment, on my 2015 list.
Klitzing wrote:First of all: the linearisation symbol of the above symmetry group you gave as "o4o3o3o4/3*a *b3d" is wrong, as the letter "d" likewise isn't a real node, rather it is a virtaul one too, which re-reffers to the d-th so far already provided real node from the left. Accordingly it ought be prefixed by an asterisk as well. So you'd write rather "o4o3o3o4/3*a *b3*d".
Thanks, I didn't realize asterisks before virtual nodes were mandatory. I guess I haven't learned all the ins and outs of the linearization rules yet.
polychoronlover wrote:x4x3x3x4/3*a *b3d
Possible name: dicroch (dicubatirhombated cubihexagonal honeycomb)
polychoronlover wrote:x4x3o3x4/3*a *b3d
Possible name: Dichac (dicubatihexacubatic honeycomb)
I don't like the idea of using "hexa-" when the hexagonal-tiling symmetry of the cell doesn't carry over into the entire pattern. In these, as in almost every other uniform honeycomb, the hexagons act like truncated triangles. So I would prefer something like "tri-", or "triati-" to reflect the o3o3o3*a symmetry, or maybe just "apeirati-" to be consistent.
I have some ideas for names:
Possible name: Dacta (dicubatitruncated apeiratic honeycomb)
Possible name: Dactapa (dicubiatitruncated prismato-apeiratic honeybomc)
I'm not entirely sure how the "x-truncated y" nomenclature emerged, or what, if anything, are the exact rules for using it, but I have a feeling these should be called apeiratitruncated dicubatic honeycomb and apeiratitruncated prismatodicubatic honeycomb. Maybe it's best to leave these ones alone for now.