In five-dimensional geometry, a 5-orthoplex, or 5-cross polytope, is a five-dimensional polytope with 10 vertices, 40 edges, 80 triangle faces, 80 tetrahedron cells, 32 5-cell hypercells.
It has two constructed forms, the first being regular with Schläfli symbol {33,4}, and the second with alternately labeled (checkerboarded) facets, with Schläfli symbol {32,1,1} or Coxeter symbol 211.
Read more about 5-orthoplex: Alternate Names, Related Polytopes, Construction, Cartesian Coordinates, Other Images, Related Polytopes and Honeycombs