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# Cantitruncated 5-cell

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)

Images

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:

(0,0,1,2,3)

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 |
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SchlĂ¤fli symbol |
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Coxeter-Dynkin diagram |
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Schlegel diagram |
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Coxeter plane projection |

Images: *Robert Webb's Great Stella software** *

Undergraduate Texts in Mathematics

Graduate Studies in Mathematics

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