Reflexive Polyhedra and their Applications in String and F-theory

TL;DR

This paper introduces reflexive polyhedra and explores their significant roles in string and F-theory physics, including mirror symmetry and dualities, along with recent classification advances.

Contribution

It provides an informal overview of reflexive polyhedra's applications in string theory and discusses recent progress in their classification.

Findings

Connection between reflexive polyhedra and mirror symmetry

Application in gauged linear sigma models

Recent classification developments

Abstract

This is an informal introduction to the concept of reflexive polyhedra and some of their most important applications in perturbative and non-perturbative string physics. Following the historical development, topics like mirror symmetry, gauged linear sigma models, and the geometrical structures relevant to string and F-theory dualities are discussed. Finally some recent developments concerning the classification of reflexive polyhedra are mentioned.