Mobility of symmetric block-and-hole polyhedra

The present approach also explains a puzzle in standard models of mobility. In the bar-joint model, a fully triangulated polyhedron is isostatic, but in a body-hinge version it is heavily overconstrained. When the bodies are panels with hinge lines intersecting at vertices, the overconstraints can be explained in local mechanical terms, with a direct symmetry description. A generalisation of the symmetry formula explains the extra states of self-stress in panel-hinge models of block-and-hole polyhedra.