orthoplex
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English[edit]
Etymology[edit]
Coined in 1991 by John Horton Conway and Neil Sloane. Blend of orthant + complex, since it has one facet for each orthant.[1]
Noun[edit]
orthoplex (plural orthoplexes)
- (geometry) A convex polytope analogous to an octahedron (3 dimensions) or 16-cell (4 dimensions).
- 1990, Mathematica Journal, volumes 1-2, page 84:
- 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.
- 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:
- It is remarkable that the four-dimensional orthoplex is the same polytope as the four-dimensional hemicube.
- 2008, John H. Conway, Heidi Burgiel, Chaim Goodman-Strauss, The Symmetries of Things, page 412:
- 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.
Synonyms[edit]
- (polytope analogous to an octahedron): cocube, cross-polytope, hyperoctahedron
Hyponyms[edit]
- (polytope analogous to an octahedron): 16-cell, 4-orthoplex, hexadecachoron, octahedron