Choreographers characteristically use both symmetry and asymmetry as part of the palette with which they compose movement sequences, and dance floor patterns and formations often display a variety of planar symmetries. Three-dimensional symmetries also appear, especially in acrobatic compositions, but also in movement arts that overlap with athletic events, such as formation skydiving. We will examine some of these three-dimensional symmetries and the ways that transitions may be designed to move from one such symmetric formation to another, looking in detail at (a) symmetries in one body, (b) three-dimensional symmetries between dancers, and (c) three-dimensional symmetry switching.