Hellenica World

# Runcitruncated 5-cell

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.

Alternative names

* Runcitruncated pentachoron
* Runcitruncated 4-simplex
* Diprismatodispentachoron
* Prip (Jonathan Bowers: for prismatorhombated pentachoron)

Images

Coordinates

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:

(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.

Name 5-cell truncated 5-cell rectified 5-cell cantellated 5-cell bitruncated 5-cell cantitruncated 5-cell runcinated 5-cell runcitruncated 5-cell omnitruncated 5-cell
SchlĂ¤fli
symbol
Coxeter-Dynkin
diagram
Schlegel
diagram
Coxeter plane projection

Images: Robert Webb's Great Stella software