The honeycomb lattice is the periodic degree-three planar graph consisting of the vertices and edges of a regular hexagonal tiling. It has two vertex classes; every edge joins opposite classes. Its planar dual graph is the triangular lattice.
The martini lattice is obtained from the honeycomb lattice by replacing every vertex in one of its two vertex classes by a triangle, attaching its three former incident bonds to the triangle's three vertices. It is a periodic degree-three planar graph, with triangular faces and nine-sided faces. Each decorated vertex and its incident bonds is a three-terminal cell with three internal triangle bonds and three terminal spokes. Its independent bond percolation threshold is , as follows from three-terminal cell partition duality.
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