Star polygons in art and culture Star polygons in art and culture Star polygons and polygonal compounds are the basis for numerous figures of significance in arts and culture. The figure may be the border or interior of the polygon, or one or more closed polygonal paths that include all of the border and also have some legs crossing the interior. Impressions of astronomical stars provide the term, but specific uses may exploit the connection or not. Stars often represent the unity of states within a country when they are used as a part of the flag. The five-pointed star, if drawn with points of equal
Hyperbolic geometry to tessellate the hyperbolic plane with regular polygons as faces. There are an infinite number of uniform tilings based on the Schwarz triangles (p q r) where 1/p + 1/q + 1/r < 1, where p,q,r are each orders of reflection symmetry at three points of the fundamental domain triangle, the symmetry group is a hyperbolic triangle group. There are also infinitely many uniform tilings that cannot be generated from Schwarz triangles, some for example requiring quadrilaterals as fundamental domains. Though hyperbolic geometry applies for any surface with a constant negative Gaussian curvature, it is usual to assume a scale