Talk:Mucubic honeycomb

Naming

I think that it would probably be more fitting if this page was moved to 'mucubic honeycomb' but we still keep petroid cubic honeycomb as an alternate name. Plasmath (talk) 14:45, 8 November 2022 (UTC)

I don't know about petroids, I am just learning from the articles here. Isn't there another 'mucubic honeycomb' of two mucubes? Is it ambiguous? Since each has only a finite facets, maybe is would be better to call them by the number like in finite polyhedra, I think of 'Rhombic dodecahedron' or 'Deltoidal hexecontahedron'. With this way, it would be called 'mucubic tetrachoron' and the other one would be called 'mucubic dichoron'. Also is possible: 'Order-4 mucubic honeycomb' and 'Order-2 mucubic honeycomb'. Cheers. 67.242.66.86 15:20, 8 November 2022 (UTC)

The mucubic dichoron is degenerate and so it isn't usually named as a honeycomb (the square tiling honeycomb is {4,4,3} and not {4,4,2}). Also, in the Polytope Discord, I'm pretty sure this polychoron has only been called the petroid cubic honeycomb once and the mucubic honeycomb around half a dozen times. I'm just thinking that we should use the more common name for this page. The mucubic honeycomb is also still a honeycomb too even though it has a finite number of cells. Plasmath (talk) 17:43, 8 November 2022 (UTC)

What makes the mucubic dihedron degenerate? I don't know what common names are used for things so if there is a common name just ignore me. It just seems saying the number of facets or the order of the ridges makes things less ambiguous, to me. Sycamore916 (talk) 18:22, 8 November 2022 (UTC)

The mucubic dichoron is a generalization of the https://polytope.miraheze.org/wiki/Dihedron, where there are two mucubes in the exact same place instead of two polygons. This is degenerate because the two cells are in the exact same location. The mucubic honeycomb is not degenerate because its 4 mucubes are all in different orientations.