# Generating 3D Figures with a Given Symmetry Group

Generating 3D Figures with a Given Symmetry Group

A symmetry of a figure is a transformation, such as a rotation, reflection, inversion, etc., that repositions the figure to be indistinguishable from the original. For example, rotating a circle about its center is a symmetry of the circle.

All the symmetries of a figure form a group called the figure's symmetry group. This Demonstration considers some figures in 3D consisting of finite sets of congruent triangles.