Alternated Order-5 Hexagonal Tiling Honeycomb
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Alternated Order-5 Hexagonal Tiling Honeycomb
In the field of Hyperbolic space, hyperbolic geometry, the order-5 hexagonal tiling honeycomb arises as one of 11 Paracompact uniform honeycombs#Regular paracompact honeycombs, regular paracompact honeycombs in 3-dimensional hyperbolic space. It is ''paracompact'' because it has Cell (geometry), cells composed of an infinite number of faces. Each cell consists of a hexagonal tiling whose vertices lie on a horosphere, a flat plane in hyperbolic space that approaches a single ideal point at infinity. The Schläfli symbol of the order-5 hexagonal tiling honeycomb is . Since that of the hexagonal tiling is , this honeycomb has five such hexagonal tilings meeting at each edge. Since the Schläfli symbol of the regular icosahedron, icosahedron is , the vertex figure of this honeycomb is an icosahedron. Thus, 20 hexagonal tilings meet at each vertex of this honeycomb.Coxeter ''The Beauty of Geometry'', 1999, Chapter 10, Table III Symmetry A lower-symmetry construction of index 120, ...
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