Four Dimensional Tops

Abstract

String theory predicts that the universe has extra dimensions, which have the structure of Calabi-Yau varieties; the universes defined by these varieties are conjectured to occur in physically indistinguishable pairs. The mathematical field of mirror symmetry seeks to understand the geometric correspondences between paired Calabi-Yau varieties. A lattice polytope is defined to be reflexive if its polar dual is also a lattice polytope. It has already been shown that reflexive polytopes can be used to describe Calabi-Yau hypersurfaces. This study looks at reflexive polytopes to gain important insight into the nature of hidden dimensions in space. Reflexive polytopes have been classified in 3D and 4D, with 4,319 and 473,800,776 classes of equivalent polytopes respectively.