I was looking for such a result in the book by Cox, Little and Schenck but I'm not able to find a proper reference.
All of the following requirements are tacitly assumed to be in the projective setting. We start with a finite set $A=[m_1,\dots,m_n] \subset M$ of characters. Attached to it we have the polytope $P=Conv(A)$ giving a projective embedding of the underlying variety $X_P$ in $\mathbb{P}^{|P \cap M|-1}$.
Now my question is the following: if we consider the linear projected variety $X_{P}^I$ associated to a subset of characters $I \subset P \cap M$, what is its associated polytope? In other words it can be possible to find a polytope $Q$ such that $X_{P}^I=X_{Q}$?
It would be useful for me to control some combinatorics about polytopes of projected projective varieties, so knowing the polytope associated would be of big help.
Thanks in advance.
