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-cells 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 or Coxeter symbol 611.
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

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

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

Images