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Combination of colored patterns and cubes for crystallographic point group visualization
Author(s) -
Nolze Gert
Publication year - 2013
Publication title -
crystal research and technology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.377
H-Index - 64
eISSN - 1521-4079
pISSN - 0232-1300
DOI - 10.1002/crat.201300134
Subject(s) - polyhedron , cube (algebra) , point group , group (periodic table) , symmetry (geometry) , symmetry operation , point (geometry) , visualization , combinatorics , homogeneous space , crystal (programming language) , crystallography , crystallographic point group , mathematics , computer science , crystal structure , geometry , physics , chemistry , artificial intelligence , quantum mechanics , programming language
A concept based on the application of a cube as a general polyhedron is presented for the visualization of point group symmetry. The cube is used to represent both the highest and lowest crystal symmetries, with differences observable as patterns characteristic to each point group. Patterns are generated using direction‐specific color keys, which enable the recognition of point group‐specific distribution of vectors in an external reference frame. For the visualization of the incoherent hexagonal crystal classes, two twinned cubes are applied in order to generate symmetry operators that would otherwise be missing. The resulting hexagonal dipyramid is described in the frame of a cube, reducing the number of used symmetry operators from 72 to 60. The complete set of 32 polyhedra are suitable, for example, as a visual aid for understanding the crystal symmetry and/or sub‐ and supergroup relationships.