9-orthoplex


In geometry, a 9-orthoplex or 9-cross polytope, is a regular 9-polytope with 18 vertices, 144 edges, 672 triangle faces, 2016 tetrahedron cells, 4032 5-cell 4-faces, 5376 5-simplex 5-faces, 4608 6-simplex 6-faces, 2304 7-simplex 7-faces, and 512 8-simplex 8-faces.
It has two constructed forms, the first being regular with Schläfli symbol, and the second with alternately labeled facets, with Schläfli symbol h or Coxeter symbol 611t.
It is one of an infinite family of /polytopes, called cross-polytopes or orthoplexes. The dual polytope is the 9-hypercube or enneract.*

Alternate names

Enneacross, derived from combining the family name cross polytope with ennea for nine in GreekPentacosidodecayotton as a 512-facetted 9-polytope. Acronym: vee

Construction

There are two Coxeter groups associated with the 9-orthoplex, one regular, dual of the enneract with the C9 or symmetry group, and a lower symmetry with two copies of 8-simplex facets, alternating, with the D9 or symmetry group.

Cartesian coordinates

Cartesian coordinates for the vertices of a 9-orthoplex, centered at the origin, are
Every vertex pair is connected by an edge, except opposites.