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
Magic hexagon triangles that point downwards (no matter how large the T-hexagon). In the above example, Magic hexagon A magic hexagon of order "n" is an arrangement of numbers in a centered hexagonal pattern with "n" cells on each edge, in such a way that the numbers in each row, in all three directions, sum to the same magic constant "M". A normal magic hexagon contains the consecutive integers from 1 to 3"n" − 3"n" + 1. It turns out that normal magic hexagons exist only for "n" = 1 (which is trivial, as it is composed of only 1 hexagon) and