Clifford algebra and the structure of point groups in higher-dimensional spaces

With the basic Clifford units being identified as mirrors, it is demonstrated how proper and improper symmetry operations of point groups in spaces of arbitrary dimensions can be parametrized. In such an approach consistency with parametrizations for groups in three dimensions can be achieved even if double groups are considered. The conversion of Clifford parameters into Cartesian matrices and vice versa is discussed and, for rotations in , also the parametrization in terms of pairs of rotations in . The formalism is illustrated by a number of examples.