the point of intersection of the line and the planes. Cn ( n > 1 ) and Cnv ( n > 1 ) cylindrical symmetry without reflection symmetry in a plane perpendicular to the axis cases in which the symmetry group is an infinite subset of that of cylindrical symmetry Point All other point groups in three dimensions No fixed points The isometry group contains translations or a screw operation. Arbitrary dimension Point One example of an isometry group, applying in every dimension, is that generated by inversion in a point. An n-dimensional parallelepiped is an example of an object invariant under such an inversion. References Slavik V. Jablan, Symmetry, Ornament and Modularity, Volume 30 of K & E Series on Knots and Everything, World Scientific, 2002. Euclidean symmetries Group theory Fixed points (mathematics) Geometric centers