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Polyhedron code

Description

A polytope code in three dimensions, i.e., a spherical code whose codewords form vertices of a polyhedron.

Cousins

  • Ball code— Polytopes dual to the hyperoctahedron, truncated octahedron, truncated cuboctahedron, and truncated icosidodecahedron are used to construct 3D ball codes.
  • \([[30,8,3]]\) Bring code— Bring code and related codes listed in [1; Table 1] arrange qubits and stabilizer generators on star polyhedra.

Member of code lists

Primary Hierarchy

Classical Domain
Spherical Kingdom
Constant-energy spherical codeECC
Spherical code
Slepian group-orbit codeECC
Polytope code
Parents
Polytope code
Three-dimensional polytope codes are polyhedron codes.
Polyhedron code
Children
Antiprism code
Cuboctahedron code
Dodecahedron code
Icosahedron code
Pentakis dodecahedron code
Rhombic dodecahedron code
Rhombicuboctahedron code
Snub-cube code

References

[1]
J. Conrad, C. Chamberland, N. P. Breuckmann, and B. M. Terhal, “The small stellated dodecahedron code and friends”, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 376, 20170323 (2018) arXiv:1712.07666 DOI
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Zoo Code ID: polyhedron

Cite as:
“Polyhedron code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2026. https://errorcorrectionzoo.org/c/polyhedron, arXiv:2606.11484
BibTeX:
@incollection{eczoo_polyhedron,
title={Polyhedron 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/polyhedron}
}
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Permanent link:
https://errorcorrectionzoo.org/c/polyhedron

Cite as:

“Polyhedron code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2026. https://errorcorrectionzoo.org/c/polyhedron, arXiv:2606.11484

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/classical/spherical/polytope/3d/polyhedron.yml.