# 6.849: Geometric Folding Algorithms: Linkages, Origami, Polyhedra (Fall 2012)

## Prof. Erik Demaine       TA: Jayson Lynch

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## Class 17 Video     [previous] [next]

 [+] Polyhedron folding: Pita forms, D-forms, seam forms, convex hull and crease properties, rolling belts, Burago-Zalgaller folding into nonconvex polyhedra. This class focuses on D-forms (introduced by artist Tony Wills) and related constructions called pita forms and seam forms: Pita forms were demonstrated in Lecture 17: take a convex polygon or curved shape and glue up two halves of its perimeter to make a convex surface. D-forms extend this to gluing together two convex polygons or curves. Seam forms further generalize to arbitrarily many, not necessarily convex polygons, but still require Alexandrov's Theorem to apply (actually a smooth version called Alexandrov-Pogorelov). We'll make physical D-forms and prove two neat properties about them (which originate from a final project in this class from 2007). We'll also briefly review rolling belts, the implementation of Bobenko-Izmestiev's Alexandrov construction, and Burago-Zalgaller's folding of any polygon with any gluing into a nonconvex polyhedron [O'Rourke 2010; Spring 2005].
 No support for video detected. Install Flash or use an HTML5 browser. Download Video: 360p, 720p Handwritten notes, page 1/3 • [previous page] • [next page] • [PDF] Handwritten notes, page 1/3 • [previous page] • [next page] • [PDF] Slides, page 1/11 • [previous page] • [next page] • [PDF] Figure 25.2 of GFALOP Slides, page 1/11 • [previous page] • [next page] • [PDF]

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