I'm planning to start a polymath project-type blog to determine the face lattice of the tridiagonal & cyclic tridiagonal Birkhoff polytopes (i.e., having dimension n-1 and n+1, respectively). There are some published results, but in my opinion, this is a underdeveloped area of math. I have some answers worked out, but I am lacking proofs. I would much prefer someone else proving the answers I've developed in the near future, than eventually proving them myself many years from now.