Geometric folding algorithms : linkages, origami, polyhedra / by Erik D. Demaine and Joseph O'Rourke.

Includes bibliographical references (p. 443-461) and index.

Introduction -- pt. 1. Linkages. Problem classification and examples -- Upper and lower bounds -- Planar linkage mechanisms -- Rigid frameworks -- Reconfiguration of chains -- Locked chains -- Interlocked chains -- Joint-constrained motion -- Protein folding -- pt. 2. Paper. Introduction -- Foundations -- Simple crease patterns -- General crease patterns -- Map folding -- Silhouettes and gift wrapping -- The tree method -- One complete straight cut -- Flattening polyhedra -- Geometric constructibility -- Rigid origami and curved creases -- pt. 3. Polyhedra. Introduction and overview -- Edge unfolding of polyhedra -- Reconstruction of polyhedra -- Shortest paths and geodesics -- Folding polygons to polyhedra -- Higher dimensions.

Folding and unfolding problems have been implicit since Albrecht Dürer in the early 1500s, but have only recently been studied in the mathematical literature. Emphasising algorithmic or computational aspects, this treatment of the geometry of folding and unfolding presents over 60 unsolved 'open problems' to spur further research.