## Polytopes and String Theory

We've investigated reflexive polygons in two dimensions. A similar construction can be used to construct reflexive

polytopesin higher dimensions. We can visualize lattice polytopes and their mirror pairs in three dimensions. Current research by Kreuzer and Skarke gives data about lattice polytopes in four and five dimensions. Algebraic geometry provides a procedure to translate from reflexive polytopes to geometric spaces.

Charles Doran, Ursula Whitcher, and Arthur Popa

Summer 2005