  We apply tropical geometry to study matrix algebras over a field with
valuation. Using the shapes of min-max convexity, known as polytropes, we
revisit the graduated orders introduced by Plesken and Zassenhaus. These are
classified by the polytrope region. We advance the ideal theory of graduated
orders by introducing their ideal class polytropes. This article emphasizes
examples and computations. It offers first steps in the geometric combinatorics
of endomorphism rings of configurations in affine buildings.
