# Reflexive Polytopes and Lattice-Polarized K3 Surfaces

## TL;DR

This paper reviews mirror symmetry for Calabi-Yau hypersurfaces and K3 surfaces, highlighting how lattice data and automorphisms help identify K3 families with high Picard rank.

## Contribution

It introduces a method to combine Picard group data and automorphisms of toric varieties to study K3 surfaces with high Picard rank.

## Key findings

- Comparison of mirror symmetry formulations for Calabi-Yau and K3 surfaces
- Identification of K3 families with high Picard rank using lattice and automorphism data
- Insights into the structure of lattice-polarized K3 surfaces

## Abstract

In this expository note, we review the standard formulation of mirror symmetry for Calabi-Yau hypersurfaces in toric varieties, and compare this construction to a description of mirror symmetry for K3 surfaces which relies on a sublattice of the Picard lattice. We then show how to combine information about the Picard group of a toric ambient space with data about automorphisms of the toric variety to identify families of K3 surfaces with high Picard rank.