Hexagon them. Coxeter states that every zonogon (a 2"m"-gon whose opposite sides are parallel and of equal length) can be dissected into "m"("m"-1)/2 parallelograms. In particular this is true for regular polygons with evenly many sides, in which case the parallelograms are all rhombi. This decomposition of a regular hexagon is based on a Petrie polygon projection of a cube, with 3 of 6 square faces. Other parallelogons and projective directions of the cube are dissected within rectangular cuboids. A regular hexagon has Schläfli symbol {6}. A regular hexagon is a part of the regular hexagonal tiling, {6,3}, with 3 hexagonal
Hexagon 12. The cube and octahedron (same as triangular antiprism) have regular skew hexagons as petrie polygons. The regular skew hexagon is the Petrie polygon for these higher dimensional regular, uniform and dual polyhedra and polytopes, shown in these skew orthogonal projections: A "principal diagonal" of a hexagon is a diagonal which divides the hexagon into quadrilaterals. In any convex equilateral hexagon (one with all sides equal) with common side "a", there exists a principal diagonal "d" such that and a principal diagonal "d" such that There is no Platonic solid made of only regular hexagons, because the hexagons tessellate, not