Regular polytope impossible ("not constructible"). The simplest few regular polygons that are impossible to construct are the "n"-sided polygons with "n" equal to 7, 9, 11, 13, 14, 18, 19, 21... Constructibility in this sense refers only to ideal constructions with ideal tools. Of course reasonably accurate approximations can be constructed by a range of methods; while theoretically possible constructions may be impractical. Euclid's "Elements" gave what amount to ruler-and-compass constructions for the five Platonic solids. (See, for example, Euclid's Elements.) However, the merely practical question of how one might draw a straight line in space, even with a ruler, might lead
Hexacontagon 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. For the "regular hexacontagon", "m"=30, and it can be divided into 435: 15 squares and 14 sets of 30 rhombs. This decomposition is based on a Petrie polygon projection of a 30-cube. A hexacontagram is a 60-sided star polygon. There are 7 regular forms given by Schläfli symbols {60/7}, {60/11}, {60/13}, {60/17}, {60/19}, {60/23}, and {60/29}, as well as 22 compound star figures with the same vertex configuration. Hexacontagon In geometry, a hexacontagon or