Cross polytope (EntityClass, 11)

From Hi.gher. Space

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 <> 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 elemental naming scheme, cross polytopes are denoted by the aero- prefix, meaning the classical element of "air".

Cross polytopes

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