  A polytrope is a tropical polytope which at the same time is convex in the
ordinary sense. A $d$-dimensional polytrope turns out to be a tropical simplex,
that is, it is the tropical convex hull of $d+1$ points. This statement is
equivalent to the known fact that the Segre product of two full polynomial
rings (over some field $K$) has the Gorenstein property if and only if the
factors are generated by the same number of indeterminates. The combinatorial
types of polytropes up to dimension three are classified.
