orthoplex en · NOUN
Pronunciation
- (US) audio
Etymology
Coined in 1991 by John Horton Conway and Neil Sloane. Blend of orthant + complex, since it has one facet for each orthant.
Meanings
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A convex polytope analogous to an octahedron (3 dimensions) or 16-cell (4 dimensions).
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: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: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:
Forms
| Spelling | Features | Labels | Source |
|---|---|---|---|
| orthoplexes | Number=Plur | lexicographic |
Deriveds
Hyponyms
16-cell (polytope analogous to an octahedron) · 4-orthoplex (polytope analogous to an octahedron) · octahedron (polytope analogous to an octahedron) · hexadecachoron (polytope analogous to an octahedron)
Relateds
Turán graph · simplex · hypercube
Synonyms
cocube (polytope analogous to an octahedron) · hyperoctahedron (polytope analogous to an octahedron) · cross-polytope (polytope analogous to an octahedron)