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Spatial symmetries occur in combination with temporal symmetries in a widerange of physical systems in nature, including time-periodic quantum systemstypically described by the Floquet formalism. In this context, groups formed bythree-dimensional point group symmetry operations in combination with timetranslation operations are discussed in this work. The derivation of these'spatio-temporal' groups from conventional point groups and their irreduciblerepresentations is outlined, followed by a complete listing. The groups arepresented in a template similar to space group operations, and are visualizedusing a modified version of conventional stereographic projections. Simpleexamples of physical processes that simultaneously exhibit symmetry in spaceand time are identified and used to illustrate the application ofspatio-temporal groups.

Spatio-temporal Symmetry - Point Groups with Time Translations