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Original Articles

From Polygons to String Theory

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Pages 343-359 | Published online: 22 Dec 2017
 

Summary

We describe special kinds of polygons, called Fano polygons or reflexive polygons, and their higher dimensional generalizations, called reflexive polytopes. Pairs of reflexive polytopes are related by an operation called polar duality. This combinatorial relationship has a deep and surprising connection to string theory: One may use reflexive polytopes to construct “mirror” pairs of geometric spaces called Calabi-Yau manifolds that could represent extra dimensions of the universe. Reflexive polytopes remain a rich source of examples and conjectures in mirror symmetry.

This article is part of the following collections:
Merten M. Hasse Prize

Additional information

Notes on contributors

Charles F. Doran

CHARLES F. DORAN received his Ph.D. from Harvard University in 1999. He is now an associate professor at the University of Alberta. As site director for the Pacific Institute of the Mathematical Sciences, he runs the Alberta Summer Math Institute for talented high school students.

Ursula A. Whitcher

URSULA A. WHITCHER received her Ph.D. from the University of Washington in 2009, and is now an assistant professor at the University of Wisconsin-Eau Claire. She enjoys working with undergraduates to research reflexive polytopes and the geometric spaces they describe.

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