On a combinatorial problem concerning subpolytopes of stack polytopes

Shephard [6] posed the problem of whether every combinatorial type of d-polytope can be represented by some subpolytope of some d-stack. Here we show that, at least in the case d=3, the answer to that problem is in the affirmative.I am indebted to Professor G.C. Shephard for reading a preliminary version of this note and making suggestions for its improvement.