Decacross

Decacross

A decacross, 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 is one of an infinite family of polytopes, called cross-polytopes or "orthoplexes". The dual polytope is the 10-hypercube or 10-cube.

The name "decacross" is derived from combining the family name "cross polytope" with "deca" for ten (dimensions) in Greek.

Construction

There are two Coxeter groups associated with the "decacross", one regular, dual of the 10-cube with the C10 or [4,38] symmetry group, and a lower symmetry with two copies of 9-simplex facets, alternating, with the D10 or [37,1,1] symmetry group.

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), (0,±1,0,0,0,0,0,0,0,0), (0,0,±1,0,0,0,0,0,0,0), (0,0,0,±1,0,0,0,0,0,0), (0,0,0,0,±1,0,0,0,0,0), (0,0,0,0,0,±1,0,0,0,0), (0,0,0,0,0,0,±1,0,0,0), (0,0,0,0,0,0,0,±1,0,0), (0,0,0,0,0,0,0,0,±1,0), (0,0,0,0,0,0,0,0,0,±1)

Every vertex pair is connected by an edge, except opposites.

See also

* Other regular 10-polytopes:
** 10-simplex (hendecaxennon) - {38}
** 10-cube (dekeract) - {4,38}
** 10-demicube (demidekeract) - {31,7,1}
* 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}
** Decacross - {38,4}

External links

*GlossaryForHyperspace | anchor=Cross | title=Cross polytope
* [http://members.cox.net/hedrondude/topes.htm Polytopes of Various Dimensions]
* [http://tetraspace.alkaline.org/glossary.htm Multi-dimensional Glossary]


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