  We present two types of self-similar shrinking solutions of positive genus
for the crystalline mean curvature flow in three dimensions analogous to the
solutions known for the standard mean curvature flow. We use them to test a
numerical implementation of a level set algorithm for the crystalline mean
curvature flow in three dimensions based on the minimizing movements scheme of
A.~Chambolle, \textit{Interfaces Free Bound.~6}~(2004). We implement a finite
element method discretization that seems to improve the handling of edges in
three dimensions compared to the standard finite difference method and
illustrate its behavior on a few examples.
