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- W2076227904 abstract "The analysis of polygonal forms and their form transitions using normal deformations [1] has been extended to a global analysis of form spaces for polygonal forms specified by N points in a plane. Coincidences of the points are explicitly allowed, and the origin of the form space is taken to correspond to a coincidence of all N points. This choice is natural since for every form there exists a totally symmetric deformation leading to exactly this configuration. The form space F for N points in a plane is a 2N-dimensional Euclidean space whose points represent all possible N-vertex polygons (simple and self-intersecting ones). By fixing the centres of gravity of the forms in the origin of the x, y plane, the dimension of the form space reduces to 2N − 2 to give a reduced form space F∗. Within the form spaces, isosymmetric manifolds (geometric loci of all forms having the same symmetry G) are determined. These manifolds inscribed in a form space F define the corresponding symmetry space S. The symmetry G (S∗) of the reduced symmetry space for three points has been determined in part. The four-dimensional symmetry group 21/04 has been found to be a subgroup of the full (noncrystallographic) symmetry of S∗. For some cases, the relation G (F∗) ⊆ G (S∗) has been exemplified." @default.
- W2076227904 created "2016-06-24" @default.
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- W2076227904 date "1995-02-01" @default.
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- W2076227904 title "Deformations, isosymmetric manifolds, and higher-dimensional form space symmetries for point ensembles (polygonal forms) under O(2) symmetry I. Two and three points" @default.
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- W2076227904 doi "https://doi.org/10.1016/0898-1221(94)00229-e" @default.
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