  We study the existence of an $n$-fold rotationally symmetric placement of a
symmetric graph in the plane allowing a continuous deformation that preserves
the symmetry and the distances between adjacent vertices. We show that such a
flexible placement exists if and only if the graph has a NAC-colouring
satisfying an additional property on the symmetry; a NAC-colouring is a
surjective edge colouring by two colours such that every cycle is either
monochromatic, or there are at least two edges of each colour.
