We prove the central limit theorem for the volume and the f-vector of the Poisson random polytope Πη in a fixed convex polytope P ⊂ ℝd. Here, Πη is the convex hull of the intersection of a Poisson process X of intensity η with P.
"Poisson polytopes." Ann. Probab. 38 (4) 1507 - 1531, July 2010. https://doi.org/10.1214/09-AOP514