Rectified Hessian polyhedron code

Description

Spherical \((6,72,1)\) code whose codewords are the vertices of the rectified Hessian complex polyhedron and the \(1_{22}\) real polytope. Codewords form the minimal lattice-shell code of the \(E_6\) lattice. The code forms a spherical 5-design [1]. See [2; pg. 127][3; pg. 126] for realizations of the 72 codewords.

Parents

Cousin

References

[1]
P. de la Harpe and C. Pache, “Spherical designs and finite group representations (some results of E. Bannai)”, European Journal of Combinatorics 25, 213 (2004) DOI
[2]
H. S. M. Coxeter. Regular Complex Polytopes. Cambridge University Press, 1991.
[3]
J. H. Conway and N. J. A. Sloane, Sphere Packings, Lattices and Groups (Springer New York, 1999) DOI
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Zoo Code ID: rect_hessian_polyhedron

Cite as:
“Rectified Hessian polyhedron code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/rect_hessian_polyhedron
BibTeX:
@incollection{eczoo_rect_hessian_polyhedron, title={Rectified Hessian polyhedron code}, booktitle={The Error Correction Zoo}, year={2022}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/rect_hessian_polyhedron} }
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Cite as:

“Rectified Hessian polyhedron code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/rect_hessian_polyhedron

Github: https://github.com/errorcorrectionzoo/eczoo_data/tree/main/codes/classical/spherical/polytope/rect_hessian_polyhedron.yml.