Enneacross
From Wikipedia, the free encyclopedia
Regular Enneacross 9-cross-polytope |
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Graph |
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Type | Regular 9-polytope |
Family | orthoplex |
Schläfli symbol | {37,4} {36,1,1} |
Coxeter-Dynkin diagrams | |
8-faces | 512 8-simplexes |
7-faces | 2304 7-simplexes |
6-faces | 4608 6-simplexes |
5-faces | 5376 5-simplexes |
4-faces | 4032 5-cells |
Cells | 2016 tetrahedra |
Faces | 672 triangles |
Edges | 144 |
Vertices | 18 |
Vertex figure | Octacross |
Symmetry group | B9, [37,4] C9, [36,1,1] |
Dual | Enneract |
Properties | convex |
An enneacross, is a regular 9-polytope with 18 vertices, 144 edges, 672 triangle faces, 2016 octahedron cells, 4032 5-cells 4-faces, 5376 5-faces, 4608 6-faces, 2304 7-faces, and 512 8-faces.
It is one of an infinite family of polytopes, called cross-polytopes or orthoplexes. The dual polytope is the 9-hypercube or enneract.
The name enneacross is derived from combining the family name cross polytope with ennea for nine (dimensions) in Greek.
Contents |
[edit] Construction
There are two Coxeter groups associated with the enneacross, one regular, dual of the enneract with the B9 or [4,37] symmetry group, and a lower symmetry with two copies of 9-simplex facets, alternating, with the C9 or [36,1,1] symmetry group.
[edit] Cartesian coordinates
Cartesian coordinates for the vertices of an enneacross, centered at the origin are
- (±1,0,0,0,0,0,0,0,0), (0,±1,0,0,0,0,0,0,0), (0,0,±1,0,0,0,0,0,0), (0,0,0,±1,0,0,0,0,0), (0,0,0,0,±1,0,0,0,0), (0,0,0,0,0,±1,0,0,0), (0,0,0,0,0,0,±1,0,0), (0,0,0,0,0,0,0,±1,0), (0,0,0,0,0,0,0,0,±1)
Every vertex pair is connected by an edge, except opposites.
[edit] See also
- Other regular 9-polytopes:
- Others in the cross-polytope family
- Octahedron - {3,4}
- Hexadecachoron - {3,3,4}
- Pentacross - {33,4}
- Hexacross - {34,4}
- Heptacross - {35,4}
- Octacross - {36,4}
- Enneacross - {37,4}
[edit] External links
- Olshevsky, George, Cross polytope at Glossary for Hyperspace.
- Polytopes of Various Dimensions
- Multi-dimensional Glossary