Possible new infinite family of uniform polytopes

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

Possible new infinite family of uniform polytopes

Postby Mecejide » Wed May 15, 2019 4:09 pm

I noticed that many of the uniform polytera with hinnic symmetry have members of the rit regiment for facets. If two of these polytera were blended, the rits (and facetings) should also blend, producing new uniform polytera. This should also work in higher dimensions. For example the blend of 2 fedandohs should have 20 hexes comboing as 10 haddets, 32 pens, and 32 tips, with the firts blending out.

Unless there's something I'm missing.
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Re: Possible new infinite family of uniform polytopes

Postby Klitzing » Wed May 15, 2019 8:22 pm

First of all we have carefully to distinguish between rit = rectified tesseract = o3o3x4o
and rat = rectified triacontaditeron = rectified 5D crosspolytope = o3x3o3o4o.

The latter one also can be given wrt. demipenteractic (hinnic) symmetry as o3o3o *b3x3o,
where hin = demipenteract (aka: hemipenteract) = x3o3o *b3o3o,
while the former likewise can be given wrt. demitesseractic (hexic) symmetry as x3o3x *b3o,
where hex = demitesseract = hexadecachoron = x3o3o4o = o3o3o *b3x.

Thus the remark of Mercejide would probably try to blend 2 identic members of hinnic symmetry,
when the 2 (assumed to be) non-identically decorated arms of the Dynkin symbol get reversed,
but the longer tail each would be kept in place: Then indeed the facets of that tail could be blendet out.

But such a blend supposedly would increase the total symmetry from demipenteractic (hinnic)
back to (full) penteractic (pentic) symmetry again. And I'd bet that Jonathan would count those there already...

--- rk
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