Jim, The rotation angles can be found from the eigenvalues, which are the n nth roots of unity. I think this derivation is in the *first edition* of Differential Equations, Dynamical Systems and Linear Algebra by Hirsch and Smale. Initially think of the rotation as on R^n tensor the complex field. Each root of unity exp(i*theta) occurs with its complex conjugate. The *real part* of the sum of their eigenspaces is invariant under the rotation, and on this 2-plane is rotation by theta. If R^n is of dimension n = 2L+1, then the orthogonal complement of (1,1,...,1) is dimension 2L, and that is what is the direct sum of invariant 2-planes. On these, the |rotation angles| are 2π*K/(2L+1) for some K in {1,2,...,L}. So: Yes, I was off by one. That denominator should have been 2L+1, not 2L. —Dan ----- I don’t understand the step near the end where you find the rotation angles (“it is easy to check”), and I don’t see how it can be correct. The permutation you describe is of order n, while the rotation you describe is of order L. Am I missing something? -----