## Description

For any spherical code whose codewords are vertices of a polytope, the dual code consists of codewords that are centers of the faces of said 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.

## Parent

## Children

- 24-cell code — The 24-cell is self-dual.
- Simplex spherical code — The simplex is self-dual.
- Polygon code — Polygons are self-dual.
- Witting polytope code — The Witting polytope is self-dual.

## Cousins

- 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.
- Icosahedron code — The icosahedron and dodecahedron are dual to each other.
- Hypercube code — Orthoplexes and hypercubes are dual to each other.

## Page edit log

- Victor V. Albert (2024-07-30) — most recent

## Cite as:

“Dual polytope code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/dual_polytope