I will introduce a class of simple polytopes, called pellytopes, due to their numbers of vertices being given by the Pell numbers. As conjectured by He—Li—Raman—Zhang, they define a set of binary geometries, which are closely related to M_{0,n}.
The pellytopes are a curious set of polytopes in another sense: they are simple, indecomposable polytopes whose faces are products of smaller pellytopes. I'll use this to give an alternative formula for the multiplicative inverse of a formal power series in terms of pellytopes and their ‘motivic interiors’.
This talk is based partly on joint work with Lara Bossinger and Máté Telek.