To echo André, it would be useful to see a definition of what you mean.  The secondary polytope is generally defined for a point configuration, not for a polytope. Here are two definitions,
the first from Carl Lee's article "Subdivisions and triangulations of polytopes" (*[Handbook of Discrete and Computational Geometry][1]*), and the second from Sven Herrmann's paper, "On the facets of the secondary polytope"
([arXiv.0908.2737v3][2]).
In the first, $V$ is a set of points in $\mathbb{R}^d$, in the second,
$\cal{A}$ is a multiset of points in $\mathbb{R}^d$.
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<img src="http://cs.smith.edu/~orourke/MathOverflow/SecondaryPolytope.jpg" alt="SecondaryPolytope" />
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Each vertex of the secondary polytope corresponds to a triangulation of the point set.

So under one interpretation (which cannot be what you intend), a simplicial polytope has just one
triangulation&mdash;itself&mdash;and so the secondary polytope consists of just that one vertex.


  [1]: http://cs.smith.edu/~orourke/books/discrete.html
  [2]: http://arxiv.org/abs/0908.2537