10.1016/0898-1221(96)00045-4

Deformations, isosymmetric manifolds, and higher dimensional form space symmetries for point ensembles (polygonal forms) under O(2) symmetry II. Four points

Abstract

AbstractPolygonal forms specified by four points in a plane and their embedding in form spaces F (full eight-dimensional and reduced six-dimensional spaces) are analysed on the lines of Part I of this paper [1]. Isosymmetric manifolds (geometric loci of forms with equal symmetry) in these form spaces are determined. The symmetry of the four-dimensional subspace Fx = (x1, x2, x3, x4) of F is found to be the 48-element group 2405 of four-dimensional crystallography. Its relationship to the symmetry Oh of the three-dimensional subspace F∗x which is orthogonal to the translation Tx is clarified. From the general symmetry operations of form spaces F for N points in En, it is deduced that F must display an n-axial symmetry (for three points in E2, a biaxial symmetry had already been found). Furthermore, the topologies of the isosymmetric manifolds in section planes and in three-dimensional subspaces of the form spaces are discussed. By considering the hierarchy of basis forms and possible transitions between them, conclusions about the manifold topology in E4 can be drawn

Similar works

Full text

thumbnail-image

Elsevier - Publisher Connector

Provided original full text link
Last time updated on 6/5/2019

This paper was published in Elsevier - Publisher Connector .

Having an issue?

Is data on this page outdated, violates copyrights or anything else? Report the problem now and we will take corresponding actions after reviewing your request.