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I have an exercise that asks me to find the h vector of a pyramid which has a d-polytope as its base, and I have no idea what to do, so I would appreciate any help, solution or intuitive approach Thank you in advance

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    With no idea how to start you must at least tell us what you know. Do you know what an $h$-vector is? Is there any polytope anywhere (perhaps in two or three dimensions) where you can compute the $h$ vector? Please edit your question to include this information. – 2017-01-24
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    Oh sorry, I know what it is but I only have a more theoretical approach. I know its type , but I dont really know how it works on given polytopes – 2017-01-24
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    Somewhere in class or in the book before you reach this exercise you should have seen some examples where $h$-vectors were computed explicitly. I think you need to update your "theoretical approach" by understanding examples. Then you can tackle the exercise. – 2017-01-24
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    actually i have that f(octahedron)=(1,4,12,8) then h(octahedron)=(1,3,3,1) as the only example in my notes – 2017-01-24

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From your comment:

You know the $h$-vector for the octahedron. Now imagine a pyramid in $\mathbb{R}^4$ constructed by choosing a point outside the three dimensional subspace containing the octahedron and joining it to all the vertices of the octahedron. You should be able to compute the $f$ and $h$-vectors of that pyramid in terms of the vectors for the octahedron.

Now generalize to a pyramid $P$ in $d+1$-space whose $d$ dimensional base $B$ is given. Then compute the $f$ and $h$-vectors of $P$ in terms of those for $B$.