## Elementary Polychora

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

### Re: Elementary Polychora

In order to get the incidences right you both missed the degenerate tet||inv tuts (tetaltuts), cf. rap||inv tip.
--- rk
Klitzing
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### Re: Elementary Polychora

Klitzing wrote:In order to get the incidences right you both missed the degenerate tet||inv tuts (tetaltuts), cf. rap||inv tip.
--- rk

Yes I saw that on your site and it took me a while to figure out the reason for needing that but I think I understand geometrically to fit them together you need medium to attach the smaller elements into a tut. I was looking at it more practically if I would cut a tip into pieces what pieces would I get.
ndl
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### Re: Elementary Polychora

The decomposition of a tut is, essentially, a 3d "analogue" of the current decomposition of the tip. They are needed as facets to connect the other pieces together and appear as facets in the segmentotopal representation. That tut decomposition consists of a tet, 4 octs, 6 tets (as line || perp line), and 4 hexagonal pyramids (again, degenerate).
Trionian

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### Re: Elementary Polychora

All of the tetrahedral uniforms can be described as "cutouts" of the tessellation 10Y4-8T. In 4D, it seems like all the pentachorics can be found in a CRF tetracomb of pen, trippy, and 4||tet elements (a decomposition of cypit). Are there other tessellations like this for other symmetries? I assume octahedral could be done with some expanded version of 10Y4-8T, so could hex/ico uniforms be done also?
ndl
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### Re: Elementary Polychora

Is tisdip (3,4 duoprism) an augmentation of squippy prism by tepe? Seems like it would be.
ndl
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### Re: Elementary Polychora

ndl wrote:Is tisdip (3,4 duoprism) an augmentation of squippy prism by tepe? Seems like it would be.

No. - Squippy prism + tet prism would be (squippy + tet) prism. And squippy + tet unites into a skew trip with 1 square (bottom of squippy) plus 2 rhombs (each built from 2 coplanar triangles). Thus your augmentation consists from 2 straight trips, 2 skew trips, 1 cube (square prism), and 2 rhomb prisms. As such it turns out to be kind a skew variant of tisdip only.
--- rk
Klitzing
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### Re: Elementary Polychora

Right. Should have realized that.
ndl
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