Augmented omnitruncated tesseract

[quickfur]

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.

[wendy]

You get a3c3a4x by selectively diminishing c3a4o3x. So your example gives a=c=x here.

[Klitzing]

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.

--- rk

[quickfur]

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...

[Klitzing]

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)


--- rk