Discrete & Computational Geometry

, Volume 55, Issue 3, pp 662–680 | Cite as

Combinatorially Two-Orbit Convex Polytopes

  • Nicholas MatteoEmail author


Any convex polytope whose combinatorial automorphism group has two orbits on the flags is isomorphic to one whose group of Euclidean symmetries has two orbits on the flags (equivalently, to one whose automorphism group and symmetry group coincide). Hence, a combinatorially two-orbit convex polytope is isomorphic to one of a known finite list, all of which are 3-dimensional: the cuboctahedron, icosidodecahedron, rhombic dodecahedron, or rhombic triacontahedron. The same is true of combinatorially two-orbit normal face-to-face tilings by convex polytopes.


Two-orbit Convex polytopes Tilings Half-regular Quasiregular 

Mathematics Subject Classification

52B15 51M20 51F15 52C22 


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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsYork UniversityTorontoCanada

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