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PART III - Polyhedra

Published online by Cambridge University Press:  05 June 2012

Joseph O’Rourke
Affiliation:
Smith College, Massachusetts
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Summary

The third and final part of this book explores folding and unfolding the surface of a polyhedron, a 3D solid shape whose surface is made of flat faces. We break the tradition of the previous two parts of always including at least one beautiful theorem in each chapter, for a central question in unfolding polyhedra has so resisted solution that there are as yet no general theorems. We explain this central open problem, “Dürer's Problem” for convex polyhedra, in the next chapter, and follow that with a variation for “orthogonal polyhedra” on which there are results to report. We close with the inverse of unfolding, folding a piece of paper to a polyhedron, which has at its core a beautiful and powerful theorem of the Russian geometer Alexandr Alexandrov. Investigation of folding polyhedra has led to many surprises and leads to several unsolved but accessible problems for the reader to ponder.

Type
Chapter
Information
How to Fold It
The Mathematics of Linkages, Origami, and Polyhedra
, pp. 99 - 100
Publisher: Cambridge University Press
Print publication year: 2011

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  • Polyhedra
  • Joseph O’Rourke, Smith College, Massachusetts
  • Book: How to Fold It
  • Online publication: 05 June 2012
  • Chapter DOI: https://doi.org/10.1017/CBO9780511975028.010
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  • Polyhedra
  • Joseph O’Rourke, Smith College, Massachusetts
  • Book: How to Fold It
  • Online publication: 05 June 2012
  • Chapter DOI: https://doi.org/10.1017/CBO9780511975028.010
Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

  • Polyhedra
  • Joseph O’Rourke, Smith College, Massachusetts
  • Book: How to Fold It
  • Online publication: 05 June 2012
  • Chapter DOI: https://doi.org/10.1017/CBO9780511975028.010
Available formats
×