Uniform Self-Dual Non-Regular Polytope

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

Uniform Self-Dual Non-Regular Polytope

I have discovered that the great icosiheptapeton (gaje) is uniform and self-dual, but not regular.
Mecejide
Trionian

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Re: Uniform Self-Dual Non-Regular Polytope

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

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).
username5243
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Re: Uniform Self-Dual Non-Regular Polytope

Are there any examples in lower dimensions?
Catisfluffy
Mononian

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Re: Uniform Self-Dual Non-Regular Polytope

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∂¬∀∃∅∆∇∈∉∋∌∏∑ ∗∘∙√∛∜∝∞∧∨∩∪∫≅≈≟≠≡≤≥⊂⊃⊆⊇ ⊕⊖⊗⊘⊙⌈⌉⌊⌋⌜⌝⌞⌟〈〉⟨⟩
mr_e_man
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