Analogues of Alexandrov's and Stoker's theorems for ball-polyhedra
  The rigidity theorems of Alexandrov (1950) and Stoker (1968) are classical results in the theory of convex polyhedra. In this paper we prove analogues of them for normal (resp., standard) ball-polyhedra. Here, a ball-polyhedron means an intersection of finitely many congruent balls in Euclidean 3-space. 
Karoly Bezdek
math.MG