This result extends Frucht's theorem that every finite group can be realized as the group of symmetries of a graph.
12.
Henri Poincar?provided the mathematical framework for relativity theory by proving that Lorentz transformations are a subset of his Poincar?group of symmetry transformations.
13.
Like the gyrobifastigium, it can fill space, but only screw symmetry, not with a full three-dimensional group of symmetries.
14.
A string not written in boldface represents a group of symmetries of the Euclidean plane, which is assumed to contain two independent translations.
15.
The symmetry of a crystal, by contrast, is described by a space group of symmetry operations, which includes translations in space.
16.
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.
17.
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.
18.
Of the uniform paracompact H 3 honeycombs, 11 are "'regular "', meaning that their group of symmetries acts transitively on their flags.
19.
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.
20.
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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