Incenter centers known to the ancient Greeks, and the only one that does not in general lie on the Euler line. It is the first listed center, X(1), in Clark Kimberling's Encyclopedia of Triangle Centers, and the identity element of the multiplicative group of triangle centers. For polygons with more than three sides, the incenter only exists for tangential polygons—those that have an incircle that is tangent to each side of the polygon. In this case the incenter is the center of this circle and is equally distant from all sides. It is a theorem in Euclidean geometry that the three
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