Binary geometries from pellytopes

TL;DR

This paper introduces a new family of binary geometries derived from pellytopes, simple polytopes with vertices counted by Pell's numbers, linking them to stringy integrals and the moduli space of curves.

Contribution

It constructs a novel class of binary geometries based on pellytopes and relates them to existing structures like the ABHY associahedron, confirming a conjecture by He--Li--Raman--Zhang.

Findings

Pellytopes have vertices counted by Pell's numbers.

A new family of binary geometries is established from pellytopes.

Connections are made between pellytopes and the moduli space of curves.

Abstract

Binary geometries have recently been introduced in particle physics in connection with stringy integrals. In this work, we study a class of simple polytopes, called \emph{pellytopes}, whose number of vertices are given by Pell's numbers. We provide a new family of binary geometries determined by pellytopes as conjectured by He--Li--Raman--Zhang. We relate this family to the moduli space of curves by comparing the pellytope to the ABHY associahedron.