Loading...
Please wait, while we are loading the content...
Similar Documents
Two– and Three–dimensional Point Groups of Hyper–tablet P–symmetries and Their Geometrical Application
| Content Provider | Semantic Scholar |
|---|---|
| Copyright Year | 2005 |
| Abstract | The paper contains the basic facts of the theory of P –symmetry and the results obtained by using two– and three–dimensional points groups of rosette, tablet and hyper-tablet P –symmetries for counting and modelling some categories of n–dimensional symmetry groups for n ≥ 4. 1. Shubnikov teaching of antisymmetry [3] is used as the basic for various new generalizations of the classical theory of symmetry and their large application in discrete geometry [4,5]. The interpretation of antisymmetry as the two–colored symmetry brought the idea of Belov multi–colored symmetry, named in [4,5] the p–symmetry. As the other generalization of antisymmetry Zamorzaev antisymmetry of different patterns (multiple antisymmetry [3]) appeared, extending the n by assigning to the points of a transformal figure not only one, but several qualitatively different signs + or -. Diverse approaches to the colored antisymmetry introduced by Pawley, Neronova and Belov, and their further generalization–cryptosymmetry of Niggli and Wondratchek are the synthesis of the both [4,5]. The mentioned generalizations of antisymmetry and colored symmetry are included in P–symmetry, using arbitrary number of color p (not only p = 2, as antisymmetry), assigned to the points of a figure, and arbitrary group P of color–permutations (not only cyclic groups, as Belov p–symmetry). The more detailed explanation of the ideas mentioned, the recent methods of applying two– and three–dimensional crystallographic groups of rosette, tablet and hyper–tablet P–symmetries to the study of multidimensional symmetry groups will be given in this communication. 90 A.F. PALISTRANT 2 2. The basic assumptions of P–symmetry, explained in details in [4,5], are the following: assigning to all the points of a figure at least one index i = 1, 2, .p, its isometrical symmetry transforming each points with the index i into the point with the index ki is called P–symmetry, where the permutation of indices |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | https://www.math.uaic.ro/~annalsmath/pdf-uri%20anale/F1(1997)/Palistrant.pdf |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
