Alternative names: Snub cuboctahedron code.
Description
Spherical \((3,24,\frac{2(t^2+1)}{3t^2+2t+2})\) code whose codewords are the vertices of a snub cube, normalized to lie on the unit sphere. Here, \(t \approx 1.839\) is the tribonacci constant, the real root of \(t^3-t^2-t-1=0\), and the minimum distance squared is approximately \(0.55384\).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.Notes
See the corresponding Bendwavy database entry [3].Member of code lists
Primary Hierarchy
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
- [3]
- R. Klitzing. “Snic.” Polytopes & their Incidence Matrices. bendwavy.org/klitzing/incmats/snic.htm
Page edit log
- Victor V. Albert (2022-11-16) — most recent
Cite as:
“Snub-cube code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/snub_cube