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Snub-cube code

Description

Spherical \((3,24,0.55384)\) code whose codewords are the vertices of a snub cube, normalized to lie on the unit sphere.

Protection

Optimal configuration of 24 points on \(S^2\) [1; pg. 78]; see also the recent discussion in [2; Sec. 1.3, Conj. 1.4], which cites Robinson’s geometric proof of optimality and asks for a semidefinite-programming proof.

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
Snub-cube code

References

[1]
T. Ericson, and V. Zinoviev, eds. Codes on Euclidean spheres. Elsevier, 2001.
[2]
H. Cohn, D. de Laat, and N. Leijenhorst, “Optimality of spherical codes via exact semidefinite programming bounds”, (2024) arXiv:2403.16874
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Zoo Code ID: snub_cube

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

Cite as:

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

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