Homework1: Suppose we have n points in the plane in general position and a line that goes through one of them. Rotate the line clockwise around point, until it hits another, then continue rotating around it and so on.
Prove that for any points set there is a starting line that hits each point infinitely many times.
Homework2: Permutahederon.
a) show that it is n-1 dimensional (we discussed why it is at most n-1 dimensional in class, here you have to show why exactly n-1 dimensional).
b) Show that it has n! vertices
c) describe all its faces
d) determine the dimensions of the faces found. In particular, show that facets correspond to the ordered partitions (A,B) of [n], A,B non empty.