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 <a_{1}a_{2}...a_{n}> 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 |
diamond • octahedron • aerochoron • aeroteron • aeropeton |