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
Hendecagram Hendecagram In geometry, a hendecagram (also endecagram or endekagram) is a star polygon that has eleven vertices. The name "hendecagram" combines a Greek numeral prefix, "hendeca-", with the Greek suffix "-gram". The "hendeca-" prefix derives from Greek ἕνδεκα (ἕν + δέκα, one + ten) meaning "eleven". The "-gram" suffix derives from γραμμῆς ("grammēs") meaning a line. There are four regular hendecagrams, which can be described by the notation Since 11 is prime, all hendecagrams are star polygons and not compound figures. As with all odd regular polygons and star polygons whose orders are not products of distinct Fermat primes, the