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Self-dual polytope code

Alternative Names: Self-reciprocal polytope code.

Description

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

Cousins

  • 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.

Member of code lists

Primary Hierarchy

Classical Domain
Spherical Kingdom
Constant-energy spherical codeECC
Spherical code
Slepian group-orbit codeECC
Polytope code
Dual polytope code
Parents
Dual polytope code
Self-dual polytope code
Children
Polygon code
Polygons are self-dual.
24-cell code
The 24-cell is self-dual.
Hessian polyhedron code
The \(2_{21}\) polytope is self-dual [1].
Witting polytope code
The Witting polytope is self-dual as a complex polytope. The \(4_{21}\) polytope is not self-dual [2].
Simplex spherical code
The simplex is self-dual.

References

[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)
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Zoo Code ID: self_dual_polytope

Cite as:
“Self-dual polytope code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2026. https://errorcorrectionzoo.org/c/self_dual_polytope, arXiv:2606.11484
BibTeX:
@incollection{eczoo_self_dual_polytope,
title={Self-dual polytope code},
booktitle={The Error Correction Zoo},
year={2026},
editor={Albert, Victor V. and Faist, Philippe},
eprint={2606.11484},
doi={10.48550/arXiv.2606.11484},
url={https://errorcorrectionzoo.org/c/self_dual_polytope}
}
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Permanent link:
https://errorcorrectionzoo.org/c/self_dual_polytope

Cite as:

“Self-dual polytope code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2026. https://errorcorrectionzoo.org/c/self_dual_polytope, arXiv:2606.11484

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