  According to Euler's relation any polytope P has as many faces of even
dimension as it has faces of odd dimension. As a generalization of this fact
one can compare the number of faces whose dimension is congruent to i modulo m
with the number of all faces of P for some positive integer m and for some 0 <
i < m+1. We show some classes of polytopes for which the above proportion is
asymptotically equal to 1/m.
