orthoplex

plural orthoplexes

1. geometryA convex polytope analogous to an octahedron (3 dimensions) or 16-cell (4 dimensions).

   It is remarkable that the four-dimensional orthoplex is the same polytope as the four-dimensional hemicube.

   1991, J. H. Conway, N. J. A. Sloane, “The Cell Structures of Certain Lattices”, in Peter Hilton, Friedrich Hirzebruch, Reinhold Remmert, editors, Miscellanea Mathematica, page 90

   2 more examples

   We made use of another way of considering the 120 cells, starting with the eight at the vertices of an orthoplex, that is, in the cells of a hypercube.

   1990, Mathematica Journal, volumes 1-2, page 84

   The combinatorics of this case apply to all members of the Gosset series; in every case, their cells are simplexes and orthoplexes, the latter appearing with only half symmetry.

   2008, John H. Conway, Heidi Burgiel, Chaim Goodman-Strauss, The Symmetries of Things, page 412

   Synonyms: cocube, cross-polytope, hyperoctahedron