Augmented omnitruncated tesseract

Discussion of known convex regular-faced polytopes, including the Johnson solids in 3D, and higher dimensions; and the discovery of new ones.

Augmented omnitruncated tesseract

Postby quickfur » Wed May 28, 2014 9:43 pm

Today, I was looking at diminishings of x3o4x3x, and suddenly realized that x3o4x3x is nothing other than x4x3x3x augmented with eight x4x3x||o4x3x's. :) Is this already known?

In any case, this means that x3o4x3x also admits a (probably maximal) metatridiminishing, another member of the 24-cell uniform metatridiminishings.
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Re: Augmented omnitruncated tesseract

Postby wendy » Thu May 29, 2014 9:14 am

You get a3c3a4x by selectively diminishing c3a4o3x. So your example gives a=c=x here.
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Re: Augmented omnitruncated tesseract

Postby Klitzing » Thu May 29, 2014 4:01 pm

Quickfur, you might read that very statement e.g. already on http://bendwavy.org/klitzing/incmats/prico.htm at the last paragraph before the incidence matrices.
It even would become obvious from the first of the provided lace cities.

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Re: Augmented omnitruncated tesseract

Postby quickfur » Thu May 29, 2014 4:14 pm

OK, thanks. Was the metatridiminishing ever considered? ;) I suppose, if I get some free time today, I should try to construct it and make some renders...
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Re: Augmented omnitruncated tesseract

Postby Klitzing » Thu May 29, 2014 4:16 pm

Btw., wrt. Wendy's annotation the other cases can be found there too!
I.e.:
Code: Select all
o3o4o3x (ico)     = o3o3o4x (tes)     + 8 oo3oo4ox&#x (pt||cube)
x3o4o3x (spic)    = o3x3o4x (srit)    + 8 xx3oo4ox&#x (oct||sirco)
o3x4o3x (srico)   = x3o3x4x (proh)    + 8 oo3xx4ox&#x (co||tic)
x3x4o3x (prico)   = x3x3x4x (gidpith) + 8 xx3xx4ox&#x (toe||girco)

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