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of ? is
: and the h-vector of ? is
:

We calculate the h-vector of the octahedron boundary (our first example) as follows:
:

So the h-vector of the boundary of the octahedron is (1, 3, 3, 1). It is not an accident this h-vector is symmetric. In fact, this happens whenever ? is the boundary of a simplicial polytope (these are the Dehn-Sommerville equations). In general, however, the h-vector of a simplicial complex is not even

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