  The cyclic polytope $C(n,d)$ is the convex hull of any $n$ points on the
moment curve ${(t,t^2,...,t^d):t \in \reals}$ in $\reals^d$. For $d' >d$, we
consider the fiber polytope (in the sense of Billera and Sturmfels) associated
to the natural projection of cyclic polytopes $\pi: C(n,d') \to C(n,d)$ which
"forgets" the last $d'-d$ coordinates. It is known that this fiber polytope has
face lattice indexed by the coherent polytopal subdivisions of $C(n,d)$ which
are induced by the map $\pi$. Our main result characterizes the triples
$(n,d,d')$ for which the fiber polytope is canonical in either of the following
two senses:
  - all polytopal subdivisions induced by $\pi$ are coherent,
  - the structure of the fiber polytope does not depend upon the choice of
points on the moment curve.
  We also discuss a new instance with a positive answer to the Generalized
Baues Problem, namely that of a projection $\pi:P\to Q$ where $Q$ has only
regular subdivisions and $P$ has two more vertices than its dimension.
