Someone once told me that all tessellations of convex polytopes in Euclidean space can be realized as the power diagram of some set of points (with appropriately associated radii). I do not think this is true, because power diagrams have the restrictive property that the line segment connecting two adjacent circle centers crosses their border between the cells at a right angle.
My question is about the converse of this fact: For a tessellation of convex polytopes in $\mathbb R^d$, if it is known that
- each polytope in the tessellation can be associated to a point such that
- the line segment between any points associated to adjacent polytopes intersects the shared boundary at a right angle,
then can the tessellation be realized as a power diagram of some set of points with appropriately associated radii?