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Pentakis dodecahedron code

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.

Primary Hierarchy

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
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Zoo Code ID: pentakis_dodecahedron

Cite as:
“Pentakis dodecahedron code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/pentakis_dodecahedron
BibTeX:
@incollection{eczoo_pentakis_dodecahedron, title={Pentakis dodecahedron code}, booktitle={The Error Correction Zoo}, year={2024}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/pentakis_dodecahedron} }
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Permanent link:
https://errorcorrectionzoo.org/c/pentakis_dodecahedron

Cite as:

“Pentakis dodecahedron code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/pentakis_dodecahedron

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/classical/spherical/polytope/3d/pentakis_dodecahedron.yml.