Re: [math-fun] Random nonempty intersection of cube and plane, revisited

The set of k-planes planes in n-space is called the affine Grassmannian; Klain and Rota call it Graff(n,k) and construct the invariant measure on it in their book “Introduction to Geometric Probability”. I’ll write more (and respond to the questions and proposals you all have posted) in the next day or two as my time permits (I’m having an unusually busy week). Jim