Analogues of Alexandrov's and Stoker's theorems for ball-polyhedra

Source: arXiv


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.

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