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 perhaps you are asking for the secondary polytope of a point set whose convex hull is a simplicial polytope?  But that can't be what you mean: a convex polygon is a [simplicial polytope][3] in $\mathbb{R}^2$ (its facets are segments, 1D simplicies), and the secondary polytope of a pentagon is not simplicial: its facets are quadrilaterals and pentagons.
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<img src="http://cs.smith.edu/~orourke/MathOverflow/PentagonAssoc.png" alt="PentagonAssoc" />
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<sub>(Image from [*Discrete and Computational Geometry*][4])</sub>


  [1]: http://cs.smith.edu/~orourke/books/discrete.html
  [2]: http://arxiv.org/abs/0908.2537
  [3]: http://en.wikipedia.org/wiki/Simplicial_polytope
  [4]: http://cs.smith.edu/~orourke/DCG/