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Square-antiprism code

Description

Spherical \((3,8,4(4-\sqrt{2})/7)\) code whose codewords are the vertices of the square antiprism [1; pg. 72].

Protection

Optimal configuration of 8 points in 3D space [1; pg. 72].

Notes

See the corresponding Bendwavy database entry [2].

Cousin

  • Hypercube code— The square antiprism can be obtained by stretching the cube and twisting the top of the cube by \(45\) degrees [1; pg. 72].

Member of code lists

Primary Hierarchy

Classical Domain
Spherical Kingdom
Constant-energy spherical codeECC
Spherical code
Slepian group-orbit codeECC
Polytope code
Polyhedron code
Antiprism code
Parents
Antiprism code
The antiprism reduces to a square antiprism for \(q=4\).
Square-antiprism code

References

[1]
T. Ericson and V. Zinoviev, eds., Codes on Euclidean Spheres (Elsevier, 2001)
[2]
R. Klitzing. “Squap.” Polytopes & their Incidence Matrices. bendwavy.org/klitzing/incmats/squap.htm
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Zoo Code ID: square_antiprism

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

Cite as:

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

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