User:Tomruen/5-cell honeycomb
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In four-dimensional Euclidean geometry, the 4-simplex honeycomb, 5-cell honeycomb or pentachoric-dispentachoric honeycomb is a space-filling tessellation honeycomb. It is composed of 5-cells and rectified 5-cells facets in a ratio of 1:1.
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4-simplex honeycomb | |
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(No image) | |
Type | Uniform 4-honeycomb |
Family | Simplectic honeycomb |
Schläfli symbol | {3[5]} |
Coxeter diagram | |
4-face types | {3,3,3} t1{3,3,3} |
Cell types | {3,3} t1{3,3} |
Face types | {3} |
Vertex figure | t0,3{3,3,3} |
Symmetry | ×2, [[3[5]]] |
Properties | vertex-transitive |
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Cells of the vertex figure are ten tetrahedrons and 20 triangular prisms, corresponding to the ten 5-cells and 20 rectified 5-cells that meet at each vertex. All the vertices lie in parallel realms in which they form alternated cubic honeycombs, the tetrahedra being either tops of the rectified 5-cell or the bases of the 5-cell, and the octahedra being the bottoms of the rectified 5-cell.[1]