Translation of Aleksandrov from the Russian

Katya Rykovanova

Theorem: Any unfolding homeomorphic to a sphere and whose angle sums are <= 2 pi glues to a closed, convex polyhedron.

This is an important theorem proved by A.D. Aleksandrov in the 1950's. It has never been translated to English. I translated the key parts of Chapter 4 of his book, which contains the theorem, from the original Russian. Prof. O'Rourke and I would work out the precise translation of mathematical terms, such as "manifold," "variety," "unfolding," "realizable," etc.

Supported by NSF

Advisor: Joseph O'Rourke