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Cuboctahedron code

Alternative names: Rectified cube code, Rectified octahedron code.

Description

Spherical \((3,12,1)\) code whose codewords are the vertices of the cuboctahedron. Codewords form the minimal lattice-shell code of the \(D_3\) face-centered cubic (fcc) lattice.

Protection

Code yields an optimal solution to the kissing problem in 3D [1].

Notes

See the corresponding Bendwavy database entry [2].

Cousins

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
Lattice-shell codeECC
Cuboctahedron codewords form the minimal shell of the \(D_3\) face-centered cubic (fcc) lattice.
Cuboctahedron code

References

[1]
K. Schütte and B. L. van der Waerden, “Das Problem der dreizehn Kugeln”, Mathematische Annalen 125, 325 (1952) DOI
[2]
R. Klitzing. “Co.” Polytopes & their Incidence Matrices. bendwavy.org/klitzing/incmats/co.htm
[3]
A. Holden, “Shapes, Space, and Symmetry”, (1971) DOI
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Zoo Code ID: cubeoctahedron

Cite as:
“Cuboctahedron code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/cubeoctahedron
BibTeX:
@incollection{eczoo_cubeoctahedron, title={Cuboctahedron code}, booktitle={The Error Correction Zoo}, year={2022}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/cubeoctahedron} }
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Permanent link:
https://errorcorrectionzoo.org/c/cubeoctahedron

Cite as:

“Cuboctahedron code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/cubeoctahedron

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