A question

Discussion of tapertopes, uniform polytopes, and other shapes with flat hypercells.

A question

Postby Mecejide » Fri May 03, 2019 10:53 pm

In general, is it possible to determine whether a given polytope can be created by holosnubbing any other polytope?
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Re: A question

Postby Klitzing » Sat May 04, 2019 8:22 am

You'd have to apply the inverse of holosnubbing.

So, just reconsider what holosnubbing does: You'll have to choose any element type of a given polytope, and apply an alternation onto those elements. Whenever this application of alternation returns to the start within the correct parity when applied around any axis of rotation symmetry, then we speak of (mere) snubbing, if there is at least one axis, where you'd have to run twice around, such that the parity condition is matched, we speak of holosnubbing. (That is, locally these procedures are indistinguishable. Rather it is a global distinction.) Then the one subset of those to be alternated elements is being kept in place, while the other one is being replaced by its "sefa" (sectioning facet underneath).

Thus wrt. holosnubbing you clearly will have to result with pairs of parallel elements (or at least: elements which are centered at the same ray from the body center), because any instance of this to be alternated element type will be both, maintained and replaced. (One within one of the two circuits.)

E.g. saddid is a holosnub of srid, where the pentagons are the to be alternated elements. Cf.
Image and Image:
the sefas here are the yellow decagons, situated parallel to the red pentagons.

So, whenever you have a polytope which offers two element types, which are both, centered on the same ray from the body center and show up the same local symmetry, then you'd be pretty close that this polytope could be obtained via holosnubbing. - The remainder is just to check, whether the other elements would provide some contradiction to this assumption, or not.

--- rk
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