Recall that in the videos, it was useful to find the angle between the rays...

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Recall that in the videos, it was useful to find the angle ß between the rays starting at the center of a polytope, and passing through the opposite ends of an edge. 1 1 n+1 n+1 9 1. For the n-dimensional simplex, hypercube, and cross polytope (for n ≥ 4), compute the angle ß (it's useful to note that if we use the n-dimensional simplex with vertices at the unit vectors in R"+1, then the center is the -)). It fine to leave your answer in terms of inverse cosine. 2. Taking as given that corresponding values of ß for the 24-cell, 600-cell and 120-cell are л/3, 1/5 and ≈ .27 radians, extend the argument we gave in videos to show there are no other regular polytopes in dimension > 5 by induction. 9... 9 n+1 point ( Recall that in the videos, it was useful to find the angle ß between the rays starting at the center of a polytope, and passing through the opposite ends of an edge. 1 1 n+1 n+1 9 1. For the n-dimensional simplex, hypercube, and cross polytope (for n ≥ 4), compute the angle ß (it's useful to note that if we use the n-dimensional simplex with vertices at the unit vectors in R"+1, then the center is the -)). It fine to leave your answer in terms of inverse cosine. 2. Taking as given that corresponding values of ß for the 24-cell, 600-cell and 120-cell are л/3, 1/5 and ≈ .27 radians, extend the argument we gave in videos to show there are no other regular polytopes in dimension > 5 by induction. 9... 9 n+1 point (

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1 For the n dimensional simplex the angle between the rays starting at the center ... View the full answer