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The vertices of the triangular tiling are the centers of the densest possible [[circle packing]].<ref name=Critchlow>Order in Space: A design source book, Keith Critchlow, p.74-75, pattern 1</ref> Every circle is in contact with 6 other circles in the packing ([[kissing number]]). The packing density is {{frac|{{pi}}|{{sqrt|12}}}} or 90.69%. Since the union of 3 A<sub>2</sub> lattices is also an A<sub>2</sub> lattice, the circle packing can be given with 3 colors of circles.
The [[voronoi cell]] of a triangular tiling is a [[hexagon]], and so the [[voronoi tessellation]], the hexagonal tiling, has a direct correspondence to the circle packings.
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