1. For the n-dimensional simplex, hypercube, and cross polytope (for n 2 4), compute the angle B (it's useful to note that if we use the n-dimensional simplex with vertices at the unit vectors in R", then the center is the point ( n+1' n+1 . . . 9 n+1 )). It fine to leave your answer in terms of inverse cosine. 2. Taking as given that corresponding values of f for the 24-cell, 600-cell and 120-cell are 7/3, it/5 and ~ .27 radians, extend the argument we gave in videos to show there are no other regular polytopes in dimension 2 5 by induction