Bieberbach groups are discrete subgroups of isometries of $\mathbf{R}^n$. These groups describe the symmetries of a crystal, are the fundamental groups of compact flat Riemannian manifolds, and have been extensively studied in math, physics, and chemistry. Connectivity is a geometric property of $C^*$-algebras that is equivalent to the unsuspension of $E$-theory of Connes and Higson. In this talk, we discuss when a Bieberbach group is connective and provide necessary and sufficient conditions for determining connectivity. This is joint work with Marius Dadarlat.