Aperiodic set of prototiles seen on the list of aperiodic sets of tiles. The underlying undecidability of the domino problem implies that there exists no systematic procedure for deciding whether a given set of tiles can tile the plane. Polygons are plane figures which are bounded by straight line segments. Regular polygons have all sides of equal length as well as all angles of equal measure. As early as AD 325, Pappus of Alexandria knew that only 3 types of regular polygons (the square, equilateral triangle, and hexagon) can fit perfectly together in repeating tessellations on a Euclidean plane. Within that plane, every triangle,
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