Cantellated 5-simplexes


In five-dimensional geometry, a cantellated 5-simplex is a convex uniform 5-polytope, being a cantellation of the regular 5-simplex.
There are unique 4 degrees of cantellation for the 5-simplex, including truncations.

Cantellated 5-simplex

The cantellated 5-simplex has 60 vertices, 240 edges, 290 faces, 135 cells, and 27 4-faces.

Alternate names

The vertices of the cantellated 5-simplex can be most simply constructed on a hyperplane in 6-space as permutations of or of. These represent positive orthant facets of the cantellated hexacross and bicantellated hexeract respectively.

Images

Bicantellated 5-simplex

Alternate names

The coordinates can be made in 6-space, as 90 permutations of:
This construction exists as one of 64 orthant facets of the bicantellated 6-orthoplex.

Images

Cantitruncated 5-simplex

Alternate names

The vertices of the cantitruncated 5-simplex can be most simply constructed on a hyperplane in 6-space as permutations of or of. These construction can be seen as facets of the cantitruncated 6-orthoplex or bicantitruncated 6-cube respectively.

Images

Bicantitruncated 5-simplex

Alternate names

The coordinates can be made in 6-space, as 180 permutations of:
This construction exists as one of 64 orthant facets of the bicantitruncated 6-orthoplex.

Images

Related uniform 5-polytopes

The cantellated 5-simplex is one of 19 uniform 5-polytopes based on the Coxeter group, all shown here in A5 Coxeter plane orthographic projections.