<P> The three types of Penrose tiling, P1--P3, are described individually below . They have many common features: in each case, the tiles are constructed from shapes related to the pentagon (and hence to the golden ratio), but the basic tile shapes need to be supplemented by matching rules in order to tile aperiodically; these rules may be described using labeled vertices or edges, or patterns on the tile faces--alternatively the edge profile can be modified (e.g. by indentations and protrusions) to obtain an aperiodic set of prototiles . </P> <P> Penrose's first tiling uses pentagons and three other shapes: a five - pointed "star" (a pentagram), a "boat" (roughly 3 / 5 of a star) and a "diamond" (a thin rhombus). To ensure that all tilings are non-periodic, there are matching rules that specify how tiles may meet each other, and there are three different types of matching rule for the pentagonal tiles . It is common to indicate the three different types of pentagonal tiles using three different colors, as in the figure above right . </P> <P> Penrose's second tiling uses quadrilaterals called the "kite" and "dart", which may be combined to make a rhombus . However, the matching rules prohibit such a combination . Both the kite and dart are composed of two triangles, called Robinson triangles, after 1975 notes by Robinson . </P> <Ul> <Li> The kite is a quadrilateral whose four interior angles are 72, 72, 72, and 144 degrees . The kite may be bisected along its axis of symmetry to form a pair of acute Robinson triangles (with angles of 36, 72 and 72 degrees). </Li> <Li> The dart is a non-convex quadrilateral whose four interior angles are 36, 72, 36, and 216 degrees . The dart may be bisected along its axis of symmetry to form a pair of obtuse Robinson triangles (with angles of 36, 36 and 108 degrees), which are smaller than the acute triangles . </Li> </Ul>

Can a tiling with exactly one point of rotational symmetry be periodic