120-cell code[1]
Alternative names: Hecatonicosachoron code, Dodecaplex code, Hyperdodecahedron code.
Description
Spherical \((4,600,(7-3\sqrt{5})/4)\) code whose codewords are the vertices of the 120-cell. See [3][2; Table 1][4; Table 3] for explicit realizations of its 600 codewords.
Notes
The 120-cell code yields improved proofs of the Bell-Kochen-Specker (BKS) theorem [2].See the corresponding Bendwavy database entry [5].Cousins
- Dual polytope code— The 600-cell and 120-cell are dual to each other.
- 24-cell code— Vertices of a 120-cell can be split up into vertices of five 600-cells [2,3], and vertices of a 600-cell can be split up into vertices of five 24-cells [3,6,7]. Therefore, vertices of a 120-cell can be split up into vertices of 25 24-cells.
- 600-cell code— Vertices of a 120-cell can be split up into vertices of five 600-cells [2,3]. The 600-cell and 120-cell are dual to each other.
Member of code lists
Primary Hierarchy
Parents
The code forms a spherical 11-design because its vertices can be divided into five 600-cells, each of which forms said design.
120-cell code
References
- [1]
- L. Kollros, “An Attempt to determine the twenty-seven Lines upon a Surface of the third Order, and to divide such Surfaces into Species in Reference to the Reality of the Lines upon the Surface”, Gesammelte Mathematische Abhandlungen 198 (1953) DOI
- [2]
- 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
- [3]
- H. S. M. Coxeter, Regular Polytopes (Courier Corporation, 1973)
- [4]
- S. Mamone, G. Pileio, and M. H. Levitt, “Orientational Sampling Schemes Based on Four Dimensional Polytopes”, Symmetry 2, 1423 (2010) DOI
- [5]
- R. Klitzing. “Hi.” Polytopes & their Incidence Matrices. bendwavy.org/klitzing/incmats/hi.htm
- [6]
- P. H. Schoute (1903). Mehrdimensionale Geometrie, Vol. 2 (Die Polytope)
- [7]
- M. Waegell and P. K. Aravind, “Critical noncolorings of the 600-cell proving the Bell–Kochen–Specker theorem”, Journal of Physics A: Mathematical and Theoretical 43, 105304 (2010) arXiv:0911.2289 DOI
Page edit log
- Shubham P. Jain (2026-05-05) — most recent
- Victor V. Albert (2022-11-23)
Cite as:
“120-cell code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2026. https://errorcorrectionzoo.org/c/120cell