Dual polytope code

Dual polytope code

Description

For a spherical code whose codewords are vertices of a convex polytope, the dual code consists of codewords corresponding to the facets of the polar dual polytope. For regular polytopes, these dual codewords can be represented by the normalized centers of the facets of the original polytope. The dual codewords make up the vertices of the polytope dual to the original polytope.

If the dual polytope is the same as the original polytope, the original polytope is said to be self-dual. Self-dual polytopes have the same number of faces as vertices.

Cousins

Dodecahedron code— The icosahedron and dodecahedron are dual to each other.
Icosahedron code— The icosahedron and dodecahedron are dual to each other.
Pentakis dodecahedron code— The pentakis dodecahedron and truncated icosahedron are dual to each other [1].
Rhombic dodecahedron code— The rhombic dodecahedron and cuboctahedron are dual to each other [1].
120-cell code— The 600-cell and 120-cell are dual to each other.
600-cell code— The 600-cell and 120-cell are dual to each other.
Rectified Hessian polyhedron code— The rectified and double Hessian polyhedra are dual to each other, analogous to the octahedron and cube.
Biorthogonal spherical code— Orthoplexes and hypercubes are dual to each other.
Hypercube code— Orthoplexes and hypercubes are dual to each other.