Description
Spherical \((3,32,(9-\sqrt{5})/6)\) code whose codewords are the vertices of the pentakis dodecahedron, the convex hull of the icosahedron and dodecahedron.Protection
Optimal antipodal configuration of 32 points in 3D space [1].Cousins
- Dual polytope code— The pentakis dodecahedron and truncated icosahedron are dual to each other [2].
- Icosahedron code— The pentakis dodecahedron is the convex hull of the icosahedron and dodecahedron. The pentakis dodecahedron and truncated icosahedron are dual to each other [2].
- Dodecahedron code— The pentakis dodecahedron is the convex hull of the icosahedron and dodecahedron.
Member of code lists
Primary Hierarchy
Parents
Vertices of the pentakis dodecahedron form a weighted spherical 9-design [3,4][5; Exam. 2.5].
Pentakis dodecahedron code
References
- [1]
- J. H. Conway, R. H. Hardin, and N. J. A. Sloane, “Packing Lines, Planes, etc.: Packings in Grassmannian Space”, (2002) arXiv:math/0208004
- [2]
- A. Holden, “Shapes, Space, and Symmetry”, (1971) DOI
- [3]
- J. M. Goethals and J. J. Seidel, “Cubature Formulae, Polytopes, and Spherical Designs”, The Geometric Vein 203 (1981) DOI
- [4]
- D. Hughes and S. Waldron, “Spherical (t,t)-designs with a small number of vectors”, Linear Algebra and its Applications 608, 84 (2021) DOI
- [5]
- S. Borodachov, P. Boyvalenkov, P. Dragnev, D. Hardin, E. Saff, and M. Stoyanova, “Energy bounds for weighted spherical codes and designs via linear programming”, (2024) arXiv:2403.07457
Page edit log
- Victor V. Albert (2024-11-28) — most recent
Cite as:
“Pentakis dodecahedron code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/pentakis_dodecahedron