In four dimensional geometry, the runcitruncated 5cell is a uniform polychoron. It is composed of 60 vertices, 150 edges, 120 faces, and 30 cells. The cells are: 5 truncated tetrahedra, 10 hexagonal prisms, 10 triangular prisms, and 5 cuboctahedra. Each vertex is surrounded by five cells: one truncated tetrahedron, two hexagonal prisms, one triangular prism, and one cuboctahedron; the vertex figure is a rectangular pyramid. Alternative names * Runcitruncated pentachoron
Coordinates The Cartesian coordinates of an origincentered runcitruncated 5cell having edge length 2 are: The vertices can be more simply constructed on a hyperplane in 5space, as the permutations of: (0,1,1,2,3) This construction is from the positive orthant facet of the runcitruncated pentacross. Related uniform polychora The runcitruncated pentachoron is one of 9 uniform polychora constructed from the [3,3,3] Coxeter group.
Images: Robert Webb's Great Stella software
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