( 1. For the n-dimensional simplex, hypercube, and cross polytope (for n > 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 R1+1, then the center is the point 1 n+1' n+1 n+1)). It fine to leave your answer in terms of inverse cosine. 2. Taking as given that corresponding values of for the 24-cell, 600-cell and 120-cell are a/3, r/5 and .27 radians, extend the argument we gave in videos to show there are no other regular polytopes in dimension > 5 by induction. ( 1. For the n-dimensional simplex, hypercube, and cross polytope (for n > 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 R1+1, then the center is the point 1 n+1' n+1 n+1)). It fine to leave your answer in terms of inverse cosine. 2. Taking as given that corresponding values of for the 24-cell, 600-cell and 120-cell are a/3, r/5 and .27 radians, extend the argument we gave in videos to show there are no other regular polytopes in dimension > 5 by induction