In four dimensional geometry, the runcitruncated 5-cell 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.
* Runcitruncated pentachoron
The Cartesian coordinates of an origin-centered runcitruncated 5-cell having edge length 2 are:
The vertices can be more simply constructed on a hyperplane in 5-space, as the permutations of:
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