Description
Spherical \((3,2q)\) code for \(q \geq 2\) whose codewords are the vertices of a \(q\)-antiprism.Protection
The antiprism vertices consists of two \(q\)-gon vertices with the \(q\)-gons rotated by \(2\pi/q\) degrees. The relative height and radii of the \(q\)-gons can be modulated while still staying on the sphere. For the case when the two \(q\)-gons are such that the \(q=2,3\) cases reduce to the tetrahedron and octahedron, respectively, the antiprism is a spherical 3-design for \(q \geq 3\), and a \(2\)-design for \(q=2\) [1]. This can be seen as a consequence of [2; Lemma 6.11].Cousins
- Spherical design— For the case when the two \(q\)-gons are such that the \(q=2,3\) cases reduce to the tetrahedron and octahedron, respectively, the antiprism is a spherical 3-design for \(q \geq 3\), and a \(2\)-design for \(q=2\) [1]. This can be seen as a consequence of [2; Lemma 6.11].
- Biorthogonal spherical code— The antiprism reduces to the octahedron for \(q=3\).
- Simplex spherical code— The antiprism reduces to the tetrahedron for \(q=2\).
Member of code lists
Primary Hierarchy
Parents
Antiprism code
Children
The antiprism reduces to a square antiprism for \(q=4\).
References
- [1]
- V. V. Albert, private communication, 2025.
- [2]
- S. Borodachov, “Odd strength spherical designs attaining the Fazekas–Levenshtein bound for covering and universal minima of potentials”, Aequationes mathematicae 98, 509 (2024) DOI
Page edit log
- Victor V. Albert (2025-12-09) — most recent
Cite as:
“Antiprism code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2025. https://errorcorrectionzoo.org/c/antiprism