1. As another example consider the group of symmetries of a square. 2. The dihedral group D 12 is the group of symmetries of a hexagon. 3. The Lorentz group is a Lie group of symmetries of the spacetime of special relativity. 4. A string written in boldface represents a group of symmetries of Euclidean 3-space. 5. Similar equations can be written for any one-parameter unitary group of symmetries of the physical system. 6. The functional measure would have to be invariant under the one parameter group of symmetry transformation as well. 7. The same function may be an invariant for one group of symmetries and equivariant for a different group of symmetries. 8. The same function may be an invariant for one group of symmetries and equivariant for a different group of symmetries . 9. The related einstein problem asks for a shape that can tile space but not with an infinite cyclic group of symmetries . 10. The effect proportional to the square of the electric field can exist only in crystals belonging to acentric point groups of symmetry .
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