10-orthoplex |
Rectified 10-orthoplex |
Birectified 10-orthoplex |
Trirectified 10-orthoplex |
Quadirectified 10-orthoplex |
Quadrirectified 10-cube |
Trirectified 10-cube |
Birectified 10-cube |
Rectified 10-cube |
10-cube |
||
| Orthogonal projections in BC10 Coxeter plane | |||
|---|---|---|---|
In ten-dimensional geometry, a rectified 10-cube is a convex uniform 10-polytope, being a rectification of the regular 10-cube.
There are 10 rectifications of the 10-cube, with the zeroth being the 10-cube itself. Vertices of the rectified 10-cube are located at the edge-centers of the 10-cube. Vertices of the birectified 10-cube are located in the square face centers of the 10-cube. Vertices of the trirectified 10-cube are located in the cubic cell centers of the 10-cube. The others are more simply constructed relative to the 10-cube dual polytpoe, the 10-orthoplex.
These polytopes are part of a family 1023 uniform 10-polytopes with BC10 symmetry.
Contents |
| Rectified 10-orthoplex | |
|---|---|
| Type | uniform 10-polytope |
| Schläfli symbol | t1{3,3,3,3,3,3,3,3,4} |
| Coxeter-Dynkin diagrams | |
| 7-faces | |
| 6-faces | |
| 5-faces | |
| 4-faces | |
| Cells | |
| Faces | |
| Edges | 46080 |
| Vertices | 5120 |
| Vertex figure | 8-simplex prism |
| Coxeter groups | C10, [4,38] D10, [37,1,1] |
| Properties | convex |
| B10 | B9 | B8 |
|---|---|---|
| [20] | [18] | [16] |
| B7 | B6 | B5 |
| [14] | [12] | [10] |
| B4 | B3 | B2 |
| [8] | [6] | [4] |
| Birectified 10-orthoplex | |
|---|---|
| Type | uniform 10-polytope |
| Schläfli symbol | t2{3,3,3,3,3,3,3,3,4} |
| Coxeter-Dynkin diagrams | |
| 7-faces | |
| 6-faces | |
| 5-faces | |
| 4-faces | |
| Cells | |
| Faces | |
| Edges | 184320 |
| Vertices | 11520 |
| Vertex figure | {4}x{36} |
| Coxeter groups | C10, [4,38] D10, [37,1,1] |
| Properties | convex |
| B10 | B9 | B8 |
|---|---|---|
| [20] | [18] | [16] |
| B7 | B6 | B5 |
| [14] | [12] | [10] |
| B4 | B3 | B2 |
| [8] | [6] | [4] |
| Trirectified 10-orthoplex | |
|---|---|
| Type | uniform 10-polytope |
| Schläfli symbol | t3{3,3,3,3,3,3,3,3,4} |
| Coxeter-Dynkin diagrams | |
| 7-faces | |
| 6-faces | |
| 5-faces | |
| 4-faces | |
| Cells | |
| Faces | |
| Edges | 322560 |
| Vertices | 15360 |
| Vertex figure | {4,3}x{35} |
| Coxeter groups | C10, [4,38] D10, [37,1,1] |
| Properties | convex |
| B10 | B9 | B8 |
|---|---|---|
| [20] | [18] | [16] |
| B7 | B6 | B5 |
| [14] | [12] | [10] |
| B4 | B3 | B2 |
| [8] | [6] | [4] |
| Quadrirectified 10-orthoplex | |
|---|---|
| Type | uniform 10-polytope |
| Schläfli symbol | t4{38,4} |
| Coxeter-Dynkin diagrams | |
| 7-faces | |
| 6-faces | |
| 5-faces | |
| 4-faces | |
| Cells | |
| Faces | |
| Edges | 322560 |
| Vertices | 13440 |
| Vertex figure | {4,3,3}x{34} |
| Coxeter groups | C10, [4,38] D10, [37,1,1] |
| Properties | convex |
| B10 | B9 | B8 |
|---|---|---|
| [20] | [18] | [16] |
| B7 | B6 | B5 |
| [14] | [12] | [10] |
| B4 | B3 | B2 |
| [8] | [6] | [4] |