Is the secondary polytope of a simplicial polytope necessarily simplicial?



Secondary Polytope Simplicial?
The secondary polytope of a simplicial polytope is not neccessarily either simplicial or simple. The secondary polytope of the cyclic 4-polytope with 8 vertices in given as an example in by Billera, Filliman, and Sturmfels in "Constructions and complexity of secondary polytopes" - Adv. Math. 83 (1990), no. 2, 155–179. It is clearly neither simplicial or simple.


