A symmetry extension of Maxwellʹs rule for rigidity of frames

A symmetry extension of Maxwellʹs rule for rigidity of frames is found. This rule subsumes and strengthens Maxwellʹs 1864 rule by requiring that the internal and external degrees of freedom of a pin-jointed structure are not only numerically equal, but are also equisymmetric. A number of special cases of Maxwellʹs original rule are studied to show the improved insight that the symmetry-adapted version can gi