  Graham and Pollak showed that the determinant of the distance matrix of a
tree $T$ depends only on the number of vertices of $T$. Graphical distance, a
function of pairs of vertices, can be generalized to ``Steiner distance'' of
sets $S$ of vertices of arbitrary size, by defining it to be the fewest edges
in any connected subgraph containing all of $S$. Here, we show that the same is
true for trees' {\em Steiner distance hypermatrix} of all odd orders, whereas
the theorem of Graham-Pollak concerns order $2$. We conjecture that the
statement holds for all even orders as well.
