10-orthoplex


In geometry, a 10-orthoplex or 10-cross polytope, 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 has two constructed forms, the first being regular with Schläfli symbol, and the second with alternately labeled facets, with Schläfli symbol or Coxeter symbol 711.
It is one of an infinite family of polytopes, called cross-polytopes or orthoplexes. The dual polytope is the 10-hypercube or 10-cube.

Alternate names

There are two Coxeter groups associated with the 10-orthoplex, one regular, dual of the 10-cube with the C10 or symmetry group, and a lower symmetry with two copies of 9-simplex facets, alternating, with the D10 or symmetry group.

Cartesian coordinates

for the vertices of a 10-orthoplex, centred at the origin are
Every vertex pair is connected by an edge, except opposites.

Images