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In four dimensional geometry, the cantitruncated 5-cell is a uniform polychoron. It is composed of 60 vertices, 120 edges, 80 faces, and 20 cells. The cells are: 5 truncated octahedra, 10 triangular prisms, and 5 truncated tetrahedra. Each vertex is surrounded by 2 truncated octahedra, one triangular prism, and one truncated tetrahedron.

Alternative names

* Cantitruncated pentachoron
* Cantitruncated 4-simplex
* Great prismatodispentachoron
* Truncated dispentachoron
* Grip (Jonathan Bowers: for great rhombated pentachoron)


The Cartesian coordinates of an origin-centered cantitruncated 5-cell having edge length 2 are:

These 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 cantitruncated pentacross.

Related uniform polychora

The cantitruncated 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
Coxeter plane projection

Images: Robert Webb's Great Stella software


Mathematics Encyclopedia

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