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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!
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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
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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
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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
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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
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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} (U
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distorted version is almost unrecognizable. They are still topologically identical.
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Use omnitruncate as basis, rather than regular/quasiregular?
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