A rigid motion consists of a combination of a translation and a rotation.

Yet, while Born's definition was not applicable on rigid bodies, it was very useful in describing rigid motions of bodies.

Suppose further that each pair of corresponding faces from P and Q are congruent to each other, i.e. equal up to a rigid motion.

Up to a relation by a rigid motion, they are equal if related by a direct isometry.

The sphere is transformed into itself by a three-parameter family of rigid motions.

A rigid motion of the framework is a motion such that, at each point in time, the framework is congruent to its original configuration.

The mathematical treatment of this paradox is similar to the treatment of Born rigid motion.

A translation can be described as a rigid motion: other rigid motions include rotations and reflections.

In the plane , we have rigid motions and their effects on ends as follows: