Lecture 17: Alexandrov's Theorem  Summary and Q&A
TL;DR
Folding polygons into polyhedra involves gluing the boundary to make a convex polyhedron, with various mathematical and algorithmic challenges.
Questions & Answers
Q: What is the main problem in folding polygons into polyhedra?
The main problem is determining whether a given polygon can be folded into a convex polyhedron.
Q: How many rolling belts can you have in a single example?
In general, you can have more than one rolling belt, but four rolling belts is the maximum.
Q: What does Alexandrov's Theorem state?
Alexandrov's Theorem states that given a convex polyhedral metric, there is a unique convex polyhedron that can be realized.
Summary & Key Takeaways

Folding polygons into polyhedra involves finding ways to glue the boundary of a given polygon to form a convex polyhedron.

There are two main problems: the decision problem and the enumeration problem.

Alexandrov's Theorem states that given a convex polyhedral metric, there is a unique convex polyhedra that can be realized.