Discrete integrable equations on face-centred cubics: consistency and Lax pairs of corner equations

A new set of discrete integrable equations, called face-centered quad was recently obtained using types interaction-round-a-face solutions the classical Yang-Baxter equation. These equations satisfy a formulation multidimensional consistency, known as consistency-around-a-face-centered-cube (CAFCC), which requires consistency an overdetermined system fourteen five-point on cubic unit cell. In this paper CAFCC is introduced where so-called type-C are centered at faces cell, whereas previously they were only corners. This allows to be regarded independent multidimensionally consistent systems higher-dimensional lattices and used establish their Lax pairs.