Rigidity of octahedral tetrahedral trusses

It is known that each octahedral-tetrahedral truss has at least one degree of freedom. We examine those that are relatively rigid, that is, that have exactly one degree of freedom. We include an automatic construction process of each relatively rigid truss that contains no hole. Necessary and sufficient conditions for a truss with one hole to be relatively rigid are derived. In the process of this characterisation we derive an analogue of the Three Axes Theorem of rigid-body mechanics. 1998 Published by Elsevier Science B.V. All rights reserved..