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.
| bgcolor=#e7dcc3 align=center colspan=3 | Truncated 5-simplex | ||
| Type | Uniform 5-polytope | ||
| Schläfli symbol | t | ||
| Coxeter-Dynkin diagram | |||
| 4-faces | 12 | 6 6 t | |
| Cells | 45 | 30 15 t | |
| Faces | 80 | 60 20 | |
| Edges | 75 | ||
| Vertices | 30 | ||
| Vertex figure | v | ||
| Coxeter group | A5 [3,3,3,3], order 720 | ||
| Properties | convex | ||
The vertices of the truncated 5-simplex can be most simply constructed on a hyperplane in 6-space as permutations of (0,0,0,0,1,2) or of (0,1,2,2,2,2). These coordinates come from facets of the truncated 6-orthoplex and bitruncated 6-cube respectively.
| bgcolor=#e7dcc3 align=center colspan=3 | bitruncated 5-simplex | ||
| Type | Uniform 5-polytope | ||
| Schläfli symbol | 2t | ||
| Coxeter-Dynkin diagram | |||
| 4-faces | 12 | 6 2t 6 t | |
| Cells | 60 | 45 15 t | |
| Faces | 140 | 80 60 | |
| Edges | 150 | ||
| Vertices | 60 | ||
| Vertex figure | v | ||
| Coxeter group | A5 [3,3,3,3], order 720 | ||
| Properties | convex | ||
The vertices of the bitruncated 5-simplex can be most simply constructed on a hyperplane in 6-space as permutations of (0,0,0,1,2,2) or of (0,0,1,2,2,2). These represent positive orthant facets of the bitruncated 6-orthoplex, and the tritruncated 6-cube respectively.
The truncated 5-simplex is one of 19 uniform 5-polytopes based on the [3,3,3,3] Coxeter group, all shown here in A5 Coxeter plane orthographic projections. (Vertices are colored by projection overlap order, red, orange, yellow, green, cyan, blue, purple having progressively more vertices)