关键词: projection body, Petty functional, polytopes, zonotopes

Abstract: We show that the volume of the projection body $\Pi(Z)$ of an $n$-dimensional zonotope $Z$ with $n+1$ generators and of volume $1$ is always exactly $2^n$. Moroever, we point out that an upper bound on the volume of $\Pi(K)$ of a centrally symmetric $n$-dimensional convex body of volume $1$ is at least $2^n (9/8)^{\lfloor n/3\rfloor}$.

Key words: projection body, Petty functional, polytopes, zonotopes