Hexagon partitioned into six equilateral triangles. Like squares and equilateral triangles, regular hexagons fit together without any gaps to "tile the plane" (three hexagons meeting at every vertex), and so are useful for constructing tessellations. The cells of a beehive honeycomb are hexagonal for this reason and because the shape makes efficient use of space and building materials. The Voronoi diagram of a regular triangular lattice is the honeycomb tessellation of hexagons. It is not usually considered a triambus, although it is equilateral. The maximal diameter (which corresponds to the long diagonal of the hexagon), "D", is twice the maximal radius
Moser spindle graph" has also been applied to a different graph, in the form of a triangle inscribed within a hexagon. As a unit distance graph, the Moser spindle is formed by two rhombi with 60 and 120 degree angles, so that the sides and short diagonals of the rhombi form equilateral triangles. The two rhombi are placed in the plane, sharing one of their acute-angled vertices, in such a way that the remaining two acute-angled vertices are a unit distance apart from each other. The eleven edges of the graph are the eight rhombus sides, the two short diagonals of the