In the example of the group of invertible square matrices we study a geometric invariant of a finite set of such matrices, the associated Mustafin variety. This arithmetic geometric object defines a convex set in the respective Bruhat-Tits building, to be investigated with number theoretic tools. The theory of orders yields a method to contract this convex set, step by step. We will understand this procedure in the language of Mustafin varieties. Interesting examples for Mustafin varieties are provided by representations of finite groups and also by the Clifford orders studied in Project A17.