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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

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 \(4_{21}\) real 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.), 2024. https://errorcorrectionzoo.org/c/self_dual_polytope
BibTeX:
@incollection{eczoo_self_dual_polytope, title={Self-dual polytope code}, booktitle={The Error Correction Zoo}, year={2024}, editor={Albert, Victor V. and Faist, Philippe}, 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.), 2024. https://errorcorrectionzoo.org/c/self_dual_polytope

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