  A complete set of N+1 mutually unbiased bases (MUBs) exists in Hilbert spaces
of dimension N = p^k, where p is a prime number. They mesh naturally with
finite affine planes of order N, that exist when N = p^k. The existence of MUBs
for other values of N is an open question, and the same is true for finite
affine planes. I explore the question whether the existence of complete sets of
MUBs is directly related to the existence of finite affine planes. Both
questions can be shown to be geometrical questions about a convex polytope, but
not in any obvious way the same question.
