Heptacross

Heptacross

A heptacross, is a regular 7-polytope with 14 vertices, 84 edges, 280 triangle faces, 560 octahedron cells, 672 5-cells "4-faces", 448 "5-faces", and 128 "6-faces".

It is a part of an infinite family of polytopes, called cross-polytopes or "orthoplexes". The dual polytope is the 7-hypercube, or hepteract.

The name "heptacross" is derived from combining the family name "cross polytope" with "hept" for seven (dimensions) in Greek.

Construction

There are two Coxeter groups associated with the "heptacross", one regular, dual of the hepteract with the C7 or [4,3,3,3,3,3] symmetry group, and a lower symmetry with two copies of 6-simplex facets, alternating, with the D7 or [34,1,1] symmetry group.

Cartesian coordinates

Cartesian coordinates for the vertices of a heptacross, centered at the origin are: (±1,0,0,0,0,0,0), (0,±1,0,0,0,0,0), (0,0,±1,0,0,0,0), (0,0,0,±1,0,0,0), (0,0,0,0,±1,0,0), (0,0,0,0,0,±1,0), (0,0,0,0,0,0,±1)

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

See also

* Other 7-polytopes:
** 7-simplex - {36}
** 7-cube (hepteract) - {4,35}
** 7-demicube (demihepteract) - {31,4,1}
** 321 polytope - {33,2,1}
** 231 polytope - {32,3,1}
** 132 polytope - {31,3,2}
* 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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