# An algorithm for the classification of smooth Fano polytopes

## TL;DR

This paper introduces an algorithm capable of classifying smooth Fano polytopes in any dimension, successfully applied to dimensions up to 7, revealing thousands of isomorphism classes.

## Contribution

The paper presents a novel algorithm for classifying smooth Fano polytopes across all dimensions, with comprehensive results for dimensions 6 and 7.

## Key findings

- 7622 classes of smooth Fano 6-polytopes identified
- 72256 classes of smooth Fano 7-polytopes identified
- Algorithm effectively classifies polytopes up to dimension 7

## Abstract

We present an algorithm that produces the classification list of smooth Fano d-polytopes for any given d. The input of the algorithm is a single number, namely the positive integer d. The algorithm has been used to classify smooth Fano d-polytopes for d<=7. There are 7622 isomorphism classes of smooth Fano 6-polytopes and 72256 isomorphism classes of smooth Fano 7-polytopes.