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- Title
Two-Orbit Convex Polytopes and Tilings.
- Authors
Matteo, Nicholas
- Abstract
We classify the convex polytopes whose symmetry groups have two orbits on the flags. These exist only in two or three dimensions, and the only ones whose combinatorial automorphism group is also two-orbit are the cuboctahedron, the icosidodecahedron, and their duals. The combinatorially regular two-orbit convex polytopes are certain 2 n-gons for each $$n \ge 2$$ . We also classify the face-to-face tilings of Euclidean space by convex polytopes whose symmetry groups have two flag orbits. There are finitely many families, tiling one, two, or three dimensions. The only such tilings which are also combinatorially two-orbit are the trihexagonal plane tiling, the rhombille plane tiling, the tetrahedral-octahedral honeycomb, and the rhombic dodecahedral honeycomb.
- Subjects
CONVEX polytopes; SYMMETRY groups; AUTOMORPHISM groups; EUCLIDEAN geometry; HONEYCOMB structures; COMBINATORICS
- Publication
Discrete & Computational Geometry, 2016, Vol 55, Issue 2, p296
- ISSN
0179-5376
- Publication type
Article
- DOI
10.1007/s00454-015-9754-2