A convex polytope gives rise to various frameworks derived e.g. from its 1-skeleton or a Schlegel diagram. We explore some rigidity related questions one might ask for such frameworks: When can a polytope be deformed while preserving its edge length (and convexity)? When are Schlegel diagrams rigid?

We then turn to a (tensegrity) framework obtained from a polytope P by replacing all edges of P by cables and by adding struts from each vertex to some common interior point of P. We show that this framework is locally rigid. Moreover, if P is centrally symmetric, then the framework is universally rigid under a central symmetry constraint. We briefly discuss how this relates to the question of reconstructing a polytope from its edge-graph.