Talk:Snub polyhedron

Use omnitruncate as basis, rather than regular/quasiregular?

I think it would be easier to show the snubs as arising from the omnitruncates. Then we only have to invoke alternation, instead of the vague "adding extra triangles around each vertex" – does not that definition exclude Miller's monster from being a true snub, even though it is in the sense that it has faces (squares) off the main symmetry axes? Double sharp (talk) 14:35, 30 March 2014 (UTC)

 Done Double sharp (talk) 15:20, 31 March 2014 (UTC)

Distortion

Many of the true geometrical alternated facetings shown in the "Snub derivation" column go through a lot of distortion when they are relaxed to become uniform (the faces distorted to become regular). In the case of the more complicated star polyhedra the amount of distortion can be so severe that the distorted version is almost unrecognizable. They are still topologically identical.

It seems as though the closer the Schwarz triangle is to being equilateral, the less distortion there is. Hence | 2 2 2 (the tetrahedron or digonal antiprism) is not distorted at all, and with | 3 3 5/2 (seside) the amount of distortion is so slight that it almost has to be pointed out to be noticeable. (The "hexagrams", or compounds of two triangles, present in seside are regular compounds in the pure alternation. During the relaxation to become uniform the compound's elements turn and are no longer regular, though the triangles are still coplanar. The same thing happens in sirsid.) Double sharp (talk) 05:12, 1 April 2014 (UTC)

I wonder if this may be the reason for the often-published wrong vertex configurations for s(3/2,3/2,5/2) and sr{3/2,5/3} (U₇₂ and U₇₄): perhaps a true alternation would give 3.3/2.3.5/3.3 for the latter, and it wouldn't be degenerate because the snub {3} are irregular while the {3} and {5/2} coming from the original r{3,5/2} are not. Presumably the huge amount of distortion that is needed to regain uniformity forces the snub triangles "inside-out", so that now everything is retrograde (or, looking at it another way, everything is prograde) and the vertex is surrounded twice. Unfortunately ever since my old computer crashed in 2016 I have only had Stella on my laptop, and using its faceting mode on these complicated uniform omnitruncates is mentally really taxing, but I'd like to see that happening for these two at least! Double sharp (talk) 04:35, 11 September 2018 (UTC)