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Home  >  Volume 30 (2015)

Rigid Motions of Some Regular Polygons by Abba Sani, pp 79 – 88
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Abstract

We examined permutations of vertices/sides of some regular shapes viewed as rigid motions. In particular, we use combinatorial techniques to enumerate symmetric permutations of vertices/ sides of an n-sided regular polygon . Our results involve:
(1) A well knownformula,   for generating the number of symmetries in an n-sided regular polygon accomplished using permutations;
(2). A new formula,   for number of ways of triangulating , (the number of ways of cutting  into triangles by connecting its vertices with straight lines); thereby providing a proof for Richard and Stanley’s conjecture that “All diagonals are flipped in a geodesics between two antipodes in exactly  ”.We also examined the set   of vertices of   as poset and proved some known theorems.
A discussion is given of lattices whose maximum length chains correspond to restricted
permutations.

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