The problem of isotropically orienting N converging vectors in space with application to radiotherapy planning

This note presents the solutions to the problem of orienting N converging vectors with a common origin in space with maximal separation for N = 3,4,...,8. With a specific definition of maximal separation, an algorithm was developed and coded which iteratively converges to the solutions. It has been suggested that these orientations might be appropriate for photon beam directions in conformal radiotherapy. When N = 4, the solution is the previously proposed tetrad geometry. The solutions for other N are discussed.