ABSTRACT
Translation is an isometry which leaves no point the same. Rotation is an isometry leaving one point invariant. Reflection is an isometry which leaves one line or plane invariant. The basic concepts of the three-dimensional symmetry are those of rotation, such as the symmetry of a flower; of inversion as in the difference between the right-hand and the left-hand; and the combination of these with each other and with direct movements in space. A glide reflection, like a translation, has no invariant points. Rotations, halfturns and translations are proper isometries: reflections and glide reflections are improper. A translation is a rotation about a point at infinity. A reflection is the special case of a glide reflection when there is no translation.
