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Star Dancers - Poster

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By Brigitte Bentele, Ron Lancaster

A STAR POLYGON can be thought of as the set of points formed by connecting the vertices of a regular polygon in a special manner, just as in the dance figure (above). For instance, the pentagram figure, as depicted by the dancers, has five vertices, and each vertex is connected to the one next to the adjacent vertex in a regular pentagon. The term “next” means a clockwise rotation with respect to the center of the regular polygon under consideration. One can generalize this statement to any star polygon: Call p the number of vertices of the regular polygon and d the number that determines how many vertices to count when constructing line segments to make the star. For example, for /i>d = 2, each vertex is connected to the second vertex, so one vertex is skipped; for d = 3, each vertex is connected to the third vertex, so two vertices are skipped. Coxeter (1969) calls this number d the density of the star polygon. He also provides a notation for star polygons, {p/d}, where p denotes the number of vertices of a regular polygon and d denotes the density. Although either degree or radian measure can be used, we have chosen the latter to reveal the underlying patterns more clearly.
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