There are unique 16 degrees of pentellations of the 6-cube with permutations of truncations, cantellations, runcinations, and sterications. The simple pentellated 6-cube is also called an expanded 6-cube, constructed by an expansion operation applied to the regular 6-cube. The highest form, the pentisteriruncicantitruncated 6-cube, is called an omnitruncated 6-cube with all of the nodes ringed. Six of them are better constructed from the 6-orthoplex given at pentellated 6-orthoplex.
| bgcolor=#e7dcc3 colspan=2 | Pentellated 6-cube | |
|---|---|---|
| Type | Uniform 6-polytope | |
| Schläfli symbol | t0,5 | |
| Coxeter-Dynkin diagram | ||
| 5-faces | ||
| 4-faces | ||
| Cells | ||
| Faces | ||
| Edges | 1920 | |
| Vertices | 384 | |
| Vertex figure | 5-cell antiprism | |
| Coxeter group | B6, [4,3,3,3,3] | |
| Properties | convex |
| bgcolor=#e7dcc3 colspan=2 | Pentitruncated 6-cube | |
|---|---|---|
| Type | uniform 6-polytope | |
| Schläfli symbol | t0,1,5 | |
| Coxeter-Dynkin diagrams | ||
| 5-faces | ||
| 4-faces | ||
| Cells | ||
| Faces | ||
| Edges | 8640 | |
| Vertices | 1920 | |
| Vertex figure | ||
| Coxeter groups | B6, [4,3,3,3,3] | |
| Properties | convex |
| bgcolor=#e7dcc3 colspan=2 | Penticantellated 6-cube | |
|---|---|---|
| Type | uniform 6-polytope | |
| Schläfli symbol | t0,2,5 | |
| Coxeter-Dynkin diagrams | ||
| 5-faces | ||
| 4-faces | ||
| Cells | ||
| Faces | ||
| Edges | 21120 | |
| Vertices | 3840 | |
| Vertex figure | ||
| Coxeter groups | B6, [4,3,3,3,3] | |
| Properties | convex |
| bgcolor=#e7dcc3 colspan=2 | Penticantitruncated 6-cube | |
|---|---|---|
| Type | uniform 6-polytope | |
| Schläfli symbol | t0,1,2,5 | |
| Coxeter-Dynkin diagrams | ||
| 5-faces | ||
| 4-faces | ||
| Cells | ||
| Faces | ||
| Edges | 30720 | |
| Vertices | 7680 | |
| Vertex figure | ||
| Coxeter groups | B6, [4,3,3,3,3] | |
| Properties | convex |
| bgcolor=#e7dcc3 colspan=2 | Pentiruncitruncated 6-cube | |
|---|---|---|
| Type | uniform 6-polytope | |
| Schläfli symbol | t0,1,3,5 | |
| Coxeter-Dynkin diagrams | ||
| 5-faces | ||
| 4-faces | ||
| Cells | ||
| Faces | ||
| Edges | 151840 | |
| Vertices | 11520 | |
| Vertex figure | ||
| Coxeter groups | B6, [4,3,3,3,3] | |
| Properties | convex |
| bgcolor=#e7dcc3 colspan=2 | Pentiruncicantellated 6-cube | |
|---|---|---|
| Type | uniform 6-polytope | |
| Schläfli symbol | t0,2,3,5 | |
| Coxeter-Dynkin diagrams | ||
| 5-faces | ||
| 4-faces | ||
| Cells | ||
| Faces | ||
| Edges | 46080 | |
| Vertices | 11520 | |
| Vertex figure | ||
| Coxeter groups | B6, [4,3,3,3,3] | |
| Properties | convex |
| bgcolor=#e7dcc3 colspan=2 | Pentiruncicantitruncated 6-cube | |
|---|---|---|
| Type | uniform 6-polytope | |
| Schläfli symbol | t0,1,2,3,5 | |
| Coxeter-Dynkin diagrams | ||
| 5-faces | ||
| 4-faces | ||
| Cells | ||
| Faces | ||
| Edges | 80640 | |
| Vertices | 23040 | |
| Vertex figure | ||
| Coxeter groups | B6, [4,3,3,3,3] | |
| Properties | convex |
| bgcolor=#e7dcc3 colspan=2 | Pentisteritruncated 6-cube | |
|---|---|---|
| Type | uniform 6-polytope | |
| Schläfli symbol | t0,1,4,5 | |
| Coxeter-Dynkin diagrams | ||
| 5-faces | ||
| 4-faces | ||
| Cells | ||
| Faces | ||
| Edges | 30720 | |
| Vertices | 7680 | |
| Vertex figure | ||
| Coxeter groups | B6, [4,3,3,3,3] | |
| Properties | convex |
| bgcolor=#e7dcc3 colspan=2 | Pentistericantitruncated 6-cube | |
|---|---|---|
| Type | uniform 6-polytope | |
| Schläfli symbol | t0,1,2,4,5 | |
| Coxeter-Dynkin diagrams | ||
| 5-faces | ||
| 4-faces | ||
| Cells | ||
| Faces | ||
| Edges | 80640 | |
| Vertices | 23040 | |
| Vertex figure | ||
| Coxeter groups | B6, [4,3,3,3,3] | |
| Properties | convex |
| bgcolor=#e7dcc3 colspan=2 | Omnitruncated 6-cube | |
|---|---|---|
| Type | width=180 | Uniform 6-polytope |
| Schläfli symbol | t0,1,2,3,4,5 | |
| Coxeter-Dynkin diagrams | ||
| 5-faces | 728: 12 t0,1,2,3,4 60 ×t0,1,2,3 × 160 ×t0,1,2 × 240 ×t0,1,2 × 192 ×t0,1,2,3 × 64 t0,1,2,3,4 | |
| 4-faces | 14168 | |
| Cells | 72960 | |
| Faces | 151680 | |
| Edges | 138240 | |
| Vertices | 46080 | |
| Vertex figure | irregular 5-simplex | |
| Coxeter group | B6, [4,3,3,3,3] | |
| Properties | convex, isogonal |
The full snub 6-cube or omnisnub 6-cube, defined as an alternation of the omnitruncated 6-cube is not uniform, but it can be given Coxeter diagram and symmetry [4,3,3,3,3]+, and constructed from 12 snub 5-cubes, 64 snub 5-simplexes, 60 snub tesseract antiprisms, 192 snub 5-cell antiprisms, 160 3-sr duoantiprisms, 240 4-s duoantiprisms, and 23040 irregular 5-simplexes filling the gaps at the deleted vertices.
These polytopes are from a set of 63 uniform 6-polytopes generated from the B6 Coxeter plane, including the regular 6-cube or 6-orthoplex.