| 10-orthoplex Decacross | |
|---|---|
 Orthogonal projection inside Petrie polygon | |
| Type | Regular 10-polytope |
| Family | Orthoplex |
| Schläfli symbol | {38,4} {37,31,1} |
| Coxeter-Dynkin diagrams |      
|
| 9-faces | 1024 {38} 
|
| 8-faces | 5120 {37} 
|
| 7-faces | 11520 {36}
|
| 6-faces | 15360 {35}
|
| 5-faces | 13440 {34}
|
| 4-faces | 8064 {33}
|
| Cells | 3360 {3,3}
|
| Faces | 960 {3}
|
| Edges | 180 |
| Vertices | 20 |
| Vertex figure | 9-orthoplex |
| Petrie polygon | Icosagon |
| Coxeter groups | C10, [38,4] D10, [37,1,1] |
| Dual | 10-cube |
| Properties | Convex, Hanner polytope |
In geometry, a 10-orthoplex or 10-cross polytope, is a regular 10-polytope with 20 vertices, 180 edges, 960 triangle faces, 3360 octahedron cells, 8064 5-cells 4-faces, 13440 5-faces, 15360 6-faces, 11520 7-faces, 5120 8-faces, and 1024 9-faces.
It has two constructed forms, the first being regular with Schläfli symbol {38,4}, and the second with alternately labeled (checker-boarded) facets, with Schläfli symbol {37,31,1} or Coxeter symbol 711.
It is one of an infinite family of polytopes, called cross-polytopes or orthoplexes. The dual polytope is the 10-hypercube or 10-cube.
