Enneacross

Enneacross

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.

Construction

There are two Coxeter groups associated with the "enneacross", one regular, dual of the enneract with the C9 or [4,37] symmetry group, and a lower symmetry with two copies of 8-simplex facets, alternating, with the D9 or [36,1,1] 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,±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.

See also

* Other regular 9-polytopes:
** 9-simplex (decayotton) - {38}
** 9-cube (enneract) - {4,37}
** 9-demicube (demienneract) - {31,6,1}
* 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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