  We develop a general method of proving that certain star configurations in
finit e-dimensional normed spaces are Steiner minimal trees. This method
generalizes the results of Lawlor and Morgan (1994) that could only be applied
to differentiable norms. The generalization uses the subdifferential calculus
from convex analysis. We apply this method to two special norms. The first
norm, occurring in the work of Cieslik, has unit ball the polar of the
difference body of the n-simplex (in dimension 3 this is the rhombic
dodecahedron). We determine the maximum degree of a given point in a Steiner
minimal tree in this norm. The proof makes essential use of extremal finite set
theory. The second norm, occuring in the work of Mark Conger (1989), is the sum
of the ell_1-norm and a small multiple of the ell_2 norm. For the second norm
we determine the maximum degree of a Steiner point.
