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

Can the software that gave accurate predictions for the cube be repurposed to predict properties (expected area, perimeter, and number of sides) for a random cross-section of a regular tetrahedron? We can derive a prediction for the expected area by dividing the volume by the mean width, but I don’t know how to compute the expected perimeter; the method I described yesterday (for the cube) shows that it’s equal to pi / (4 sqrt(3)) times the expected number of sides, but I don’t know how to compute the expected number of sides. Jim Propp