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Dual polytope code

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.

Cousins

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Primary Hierarchy

Parents
Dual polytope code
Children
Polygons are self-dual.
The 24-cell is self-dual.
The Witting polytope is self-dual.
The simplex is self-dual.
Page edit log

Cite as:

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

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/classical/spherical/polytope/dual_polytope.yml.