Cross polytope (EntityClass, 11)
From Hi.gher. Space
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Under the [[Tamfang naming scheme]], cross polytopes are denoted by the ''aero-'' prefix, meaning the classical element of "air". | Under the [[Tamfang naming scheme]], cross polytopes are denoted by the ''aero-'' prefix, meaning the classical element of "air". | ||
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Revision as of 17:15, 30 May 2010
A cross polytope is an n-dimensional polytope which is the dual of that dimension's hypercube. They exist non-trivially in all dimensionalities of at least three, with the two-dimensional cross polytope being a rotated square. They can be represented by the bracketopic string <a1a2...an> or by the combined Coxeter-Dynkin string o4(o3)+x.
In all dimensions above 4, the cross polytope is the regular polytope with the highest facet count.
Under the Tamfang naming scheme, cross polytopes are denoted by the aero- prefix, meaning the classical element of "air".
| Cross polytopes |
| diamond • octahedron • aerochoron • aeroteron • aeropeton |
