Truncated 5-simplexes


In five-dimensional geometry, a truncated 5-simplex is a convex uniform 5-polytope, being a truncation of the regular 5-simplex.
There are unique 2 degrees of truncation. Vertices of the truncation 5-simplex are located as pairs on the edge of the 5-simplex. Vertices of the bitruncation 5-simplex are located on the triangular faces of the 5-simplex.

Truncated 5-simplex

The truncated 5-simplex has 30 vertices, 75 edges, 80 triangular faces, 45 cells, and 12 4-faces.

Alternate names

Coordinates

The vertices of the truncated 5-simplex can be most simply constructed on a hyperplane in 6-space as permutations of or of. These coordinates come from facets of the truncated 6-orthoplex and bitruncated 6-cube respectively.

Bitruncated 5-simplex

Alternate names

  • Bitruncated hexateron

Coordinates

The vertices of the bitruncated 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 bitruncated 6-orthoplex, and the tritruncated 6-cube respectively.

Related uniform 5-polytopes

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