Reduction of quad-equations consistent around a cuboctahedron I: additive case

Abstract

In this paper, we consider a reduction of a new system of partial difference equations, which was obtained in our previous paper (Joshi and Nakazono, arXiv:1906.06650) and shown to be consistent around a cuboctahedron. We show that this system reduces to $A_2^{(1)\ast}$-type discrete Painlev\'e equations by considering a periodic reduction of a three-dimensional lattice constructed from overlapping cuboctahedra.