group of symmetries in a sentence

This result extends Frucht's theorem that every finite group can be realized as the group of symmetries of a graph.
Henri Poincar?provided the mathematical framework for relativity theory by proving that Lorentz transformations are a subset of his Poincar?group of symmetry transformations.
Like the gyrobifastigium, it can fill space, but only screw symmetry, not with a full three-dimensional group of symmetries.
A string not written in boldface represents a group of symmetries of the Euclidean plane, which is assumed to contain two independent translations.
The symmetry of a crystal, by contrast, is described by a space group of symmetry operations, which includes translations in space.

With every geometry, Klein associated an underlying groups of symmetries from the geometries, the relationships between them can be re-established at the group level.
Its full automorphism group is isomorphic to the dihedral group D 8 of order 16, the group of symmetries of an octagon, including both rotations and reflections.
Of the uniform paracompact H 3 honeycombs, 11 are "'regular "', meaning that their group of symmetries acts transitively on their flags.
Despite the fact that some crystal groups of symmetry are devoid of the center of anti-inversion, they also don t have QMR because of action of other operators of symmetry.
The full automorphism group of the Gr�tzsch graph is isomorphic to the dihedral group D 5 of order 10, the group of symmetries of a regular pentagon, including both rotations and reflections.

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