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
Dehn plane is π. This is Dehn's semi-Euclidean geometry. It is discussed in . In the same paper, Dehn also constructed an example of a non-Legendrian geometry where there are infinitely many lines through a point not meeting another line, but the sum of the angles in a triangle exceeds π. Riemann's elliptic geometry over Ω("t") consists of the projective plane over Ω("t"), which can be identified with the affine plane of points ("x":"y":1) together with the "line at infinity", and has the property that the sum of the angles of any triangle is greater than π The non-Legendrian geometry consists of