Uniform Self-Dual Non-Regular Polytope

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

Uniform Self-Dual Non-Regular Polytope

Postby Mecejide » Sun Apr 26, 2020 12:17 am

I have discovered that the great icosiheptapeton (gaje) is uniform and self-dual, but not regular.
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Re: Uniform Self-Dual Non-Regular Polytope

Postby Klitzing » Sun Apr 26, 2020 8:01 am

just for recap: what is gaje?
--- rk
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Re: Uniform Self-Dual Non-Regular Polytope

Postby username5243 » Sun Apr 26, 2020 11:25 am

Gaje (great icosaheptapeton) is one of three noble members of the jak regiment (it's number 162 on http://www.polytope.net/hedrondude/primary6.htm). Its facets are 27 hits (which is in turn the noble member of the hin regiment).
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Re: Uniform Self-Dual Non-Regular Polytope

Postby Catisfluffy » Thu Apr 30, 2020 11:03 pm

Are there any examples in lower dimensions?
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Re: Uniform Self-Dual Non-Regular Polytope

Postby mr_e_man » Thu Apr 30, 2020 11:31 pm

I thought of some tilings on a flat torus (with unequal length and width), but I later realized that the faces are not regular, depending on definitions (local vs global isometries; whether a square can rotate 90° when the space itself cannot).

Anyway, you were probably looking for something in Euclidean space, not on a flat torus....
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ℕℤℚℝℂ∂¬∀∃∅∆∇∈∉∋∌∏∑ ∗∘∙√∛∜∝∞∧∨∩∪∫≅≈≟≠≡≤≥⊂⊃⊆⊇ ⊕⊖⊗⊘⊙⌈⌉⌊⌋⌜⌝⌞⌟〈〉⟨⟩
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