Alternative names: Hexagonal tiling.
Description
A two-dimensional point set whose points are vertices of hexagons. It is not a lattice since its points do not form a group under addition. As a tiling, its dual (whose points lie at the centers of each triangle) is the triangular tiling. The ruby tiling is a fattened honeycomb tiling interpolating between the honeycomb tiling and triangular lattice.Cousins
- \(A_2\) triangular lattice— The Voronoi cell of the triangular lattice (honeycomb tiling) is a hexagon (triangle). Triangular and hexagonal tilings are dual to each other as tilings, i.e., the vertices of one tiling lie at the centers of faces of the other. Points of the honeycomb tiling form two triangular lattices. The ruby tiling is a fattened honeycomb tiling interpolating between the honeycomb tiling and triangular lattice.
- Polygon code— The Voronoi cell of the honeycomb tiling is the triangle.
- XYZ ruby Floquet code— The XYZ ruby Floquet code is defined on the ruby tiling.
- Honeycomb Floquet code— The honeycomb Floquet code is defined on the honeycomb tiling.
- Truncated trihexagonal (4.6.12) color code— The 4.6.12 (truncated trihexagonal or square-hexagon-dodecagon) tiling is obtained by applying a fattening procedure to the honeycomb tiling [1].
- Honeycomb (6.6.6) color code— The triangular color code is defined on the honeycomb tiling.
- Kitaev honeycomb code— The Kitaev honeycomb model is defined on the honeycomb tiling.
Member of code lists
Primary Hierarchy
References
- [1]
- H. Bombin and M. A. Martin-Delgado, “Exact topological quantum order inD=3and beyond: Branyons and brane-net condensates”, Physical Review B 75, (2007) arXiv:cond-mat/0607736 DOI
Page edit log
- Victor V. Albert (2025-01-03) — most recent
Cite as:
“Honeycomb tiling”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2025. https://errorcorrectionzoo.org/c/honeycomb