Self-dual polytope code

Alternative names: Self-reciprocal polytope code.

Description

A spherical code whose codewords are the vertices of a self-dual polytope.

Unimodular lattice— Self-dual polytope codes are spherical analogues of self-dual lattices.
Self-dual linear code— Self-dual polytope codes are spherical analogues of self-dual linear codes.

Parents

Self-dual polytope code

Children

Polygons are self-dual.

The 24-cell is self-dual.

The \(2_{21}\) polytope is self-dual [1].

The Witting polytope is self-dual as a complex polytope. The \(4_{21}\) polytope is not self-dual [2].

The simplex is self-dual.

[1]: H. S. M. Coxeter, “The Polytope 2 21 Whose Twenty-Seven Vertices Correspond to the Lines to the General Cubic Surface”, American Journal of Mathematics 62, 457 (1940) DOI
[2]: H. S. M. Coxeter, Regular Polytopes (Courier Corporation, 1973)

Page edit log

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