What does "orthoplex" mean?

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

What is a synonym for "orthoplex"?

Common synonyms include: cocube, cocube, cross-polytope, hyperoctahedron.

Orthoplex

noun

noun ·Rare ·Advanced level

Definitions

Noun

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

Synonyms

All synonyms

cocube cocube cross-polytope hyperoctahedron

Example

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."

Etymology

Coined in 1991 by John Horton Conway and Neil Sloane. Blend of orthant + complex, since it has one facet for each orthant.

Related phrases

4-orthoplex 16 cell turán graph

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Data sourced from Wiktionary, WordNet, CMU, and other open linguistic databases. Updated March 2026.