Pentacross
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| Regular pentacross 5-cross-polytope |
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|---|---|
 Graph |
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| Type | Regular polyteron |
| Schläfli symbol | {3,3,3,4} |
| Coxeter-Dynkin diagrams |     |
| Hypercells | 32 16-cells |
| Cells | 80 octahedra |
| Faces | 80 triangles |
| Edges | 40 |
| Vertices | 10 |
| Vertex figure | 5-cells in a 16-cell figure |
| Symmetry group | B5, [3,3,3,4] |
| Dual | Penteract |
| Properties | convex |
A pentacross, also called a triacontakaiditeron, is a five dimensional polytope with 10 vertices, 40 edges, 80 triangle faces, 80 octahedron cells, 32 5-cell hypercells.
It is a part of an infinite family of polytopes, called cross-polytopes. The dual polytope can be called a penteract, in the family of hypercubes.
The name pentacross is derived from combining the family name cross polytope with pente for five (dimensions) in Greek.
[edit] Cartesian coordinates
Cartesian coordinates for the vertices of a pentacross, centered at the origin are
- (±1,0,0,0,0), (0,±1,0,0,0), (0,0,±1,0,0), (0,0,0,±1,0), (0,0,0,0,±1)
[edit] See also
- Other regular 5-polytopes:
- Others in the cross-polytope family
- Octahedron - {3,4}
- Hexadecachoron - {3,3,4}
- Pentacross - {3,3,3,3}
- Hexacross - {3,3,3,3,4}
- Heptacross - {3,3,3,3,3,4}
- Tesseract
[edit] External links
- Olshevsky, George, Cross polytope at Glossary for Hyperspace.
- Polytopes of Various Dimensions
- Multi-dimensional Glossary
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