10-polytopes

E9 honeycomb

In geometry, an E9 honeycomb is a tessellation of uniform polytopes in hyperbolic 9-dimensional space. , also (E10) is a paracompact hyperbolic group, so either facets or vertex figures will not be bounded. E10 is last of the series of Coxeter groups with a bifurcated Coxeter-Dynkin diagram of lengths 6,2,1. There are 1023 unique E10 honeycombs by all combinations of its Coxeter-Dynkin diagram. There are no regular honeycombs in the family since its Coxeter diagram is a nonlinear graph, but there are three simplest ones, with a single ring at the end of its 3 branches: 621, 261, 162. (Wikipedia).

E9 honeycomb
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9-simplex | 5-simplex | 1 22 polytope | Uniform 2 k1 polytope | Face (geometry) | 9-demicube | Vertex figure | Wythoff construction | E8 polytope | 7-simplex | 3 21 polytope | 16-cell | Schläfli symbol | Hyperplane | Facet (geometry) | Harold Scott MacDonald Coxeter | Tetrahedron | Simplex | 8-simplex | Regular polytope | En (Lie algebra) | 1 42 polytope | 2 51 honeycomb | 5-cell | 6-simplex | Coxeter group | E6 polytope | Uniform 1 k2 polytope | 1 52 honeycomb | 2 41 polytope | Geometry | Triangle | 5 21 honeycomb | Uniform polytope | 9-orthoplex | 1 32 polytope | Semiregular polytope