Alternative Names: Granatahedron code.
Description
Spherical \((3,14,2-2/\sqrt{3})\) code whose codewords are the normalized vertices of the rhombic dodecahedron. Equivalently, the codewords are the union of the vertices of a cube and an octahedron on the unit sphere.Protection
Optimal antipodal configuration of 14 points in 3D space [1].Notes
See the corresponding Bendwavy database entry [2].Cousins
- Dual polytope code— The rhombic dodecahedron and cuboctahedron are dual to each other [3].
- Cuboctahedron code— The rhombic dodecahedron and cuboctahedron are dual to each other [3].
- Hypercube code— The vertices of a rhombic dodecahedron are a union of the vertices of a cube and an octahedron.
- Biorthogonal spherical code— The vertices of a rhombic dodecahedron are a union of the vertices of a cube and an octahedron.
- \(D_3\) face-centered cubic (fcc) lattice— The Voronoi cell of the \(D_3\) fcc lattice is a rhombic dodecahedron [4; Ch. 21, pg. 464].
- \([[14,3,3]]\) Rhombic dodecahedron surface code— The qubits of the \([[14,3,3]]\) rhombic dodecahedron surface code lie on the vertices of the small rhombic dodecahedron.
Member of code lists
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]
- R. Klitzing, “Rhode”, Polytopes & their Incidence Matrices URL
- [3]
- A. Holden, “Shapes, Space, and Symmetry”, (1971) DOI
- [4]
- J. H. Conway and N. J. A. Sloane, Sphere Packings, Lattices and Groups (Springer New York, 1999) DOI
Page edit log
- Victor V. Albert (2026-06-08) — most recent
- Victor V. Albert (2025-07-16)
Cite as:
“Rhombic dodecahedron code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2026. https://errorcorrectionzoo.org/c/rhombic_dodecahedron, arXiv:2606.11484