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Rhombicuboctahedron code

Alternative Names: Small rhombicuboctahedron code, Expanded octahedron code, Expanded cube code.

Description

Spherical \((3,24,4/(5+2 \sqrt{2}))\) code whose codewords are the vertices of the rhombicuboctahedron.

Protection

Optimal antipodal configuration of 24 points in 3D space [1].

Notes

See the corresponding Bendwavy database entry [2].

Member of code lists

Primary Hierarchy

Classical Domain
Spherical Kingdom
Constant-energy spherical codeECC
Spherical code
Slepian group-orbit codeECC
Polytope code
Polyhedron code
Parents
Polyhedron code
Rhombicuboctahedron code

References

[1]
J. H. Conway, R. H. Hardin, and N. J. A. Sloane, “Packing Lines, Planes, etc.: Packings in Grassmannian Space”, (2002) arXiv:math/0208004
[2]
R. Klitzing, “Sirco”, Polytopes & their Incidence Matrices URL
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Zoo Code ID: rhombicuboctahedron

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

Cite as:

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

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