Group Analysis of Differential Equations and Integrable Systems − 2018 Pavlos Kassotakis (University of Cyprus, Nicosia, Cyprus) Difference systems in bond and face variables and non-potential versions of discrete integrable systems Abstract: Integrable discrete scalar equations defined on a two or a three dimensional lattice can be rewritten as difference systems in bond variables or in face variables respectively. Both the difference systems in bond variables and the difference systems in face variables can be regarded as vector versions of the original equations. As an outcome, we are able to link some of the discrete equations by difference substitutions and reveal the non-potential versions of some consistent-around-the-cube quad equations. We obtain higher-point configurations, including pairs of compatible six points schemes on the ${\mathbb Z}^2$ lattice together with associated seven points schemes. As well as we obtain a variety of compatible ten point schemes together with associated ten and twelve point schemes on the ${\mathbb Z}^3$ lattice. We also present multiquadratic quad relations.