120-cell code

Description

Spherical \((4,600,(7-3\sqrt{5})/4)\) code whose codewords are the vertices of the 120-cell. The code forms a spherical 11-design because its vertices can be divided into five 600-cells, each of which forms said design. See [1; Table 1][2][3; Table 3] for realizations of the 600 codewords.

Realizations

Improved proofs of the Bell-Kochen-Specker (BKS) theorem [1].

Parent

Child

  • 600-cell code — Vertices of a 120-cell can be split up into vertices of five 600-cells [2][1].

References

[1]
M. Waegell and P. K. Aravind, “Parity Proofs of the Kochen–Specker Theorem Based on the 120-Cell”, Foundations of Physics 44, 1085 (2014) arXiv:1309.7530 DOI
[2]
H. S. M. Coxeter. Regular polytopes. Courier Corporation, 1973.
[3]
S. Mamone, G. Pileio, and M. H. Levitt, “Orientational Sampling Schemes Based on Four Dimensional Polytopes”, Symmetry 2, 1423 (2010) DOI
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Zoo Code ID: 120cell

Cite as:
“120-cell code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/120cell
BibTeX:
@incollection{eczoo_120cell, title={120-cell code}, booktitle={The Error Correction Zoo}, year={2022}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/120cell} }
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Permanent link:
https://errorcorrectionzoo.org/c/120cell

Cite as:

“120-cell code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/120cell

Github: https://github.com/errorcorrectionzoo/eczoo_data/tree/main/codes/classical/spherical/polytope/120cell.yml.