I know how to compute the content of orthoschemes in 3- and 4-dimensional spherical space from dihedral angles using Schlafli series computations. Can anyone direct me to a textbook description of the general computation in 5- or higher dimensional spherical space? I understand it probably involves iterated integrals, but I would like to see a detailed example such as might be given in a textbook.

It would also be helpful to know of any off-the-shelf software that performs such computations. Also, any tabulated listing of contents of 5-D and/or higher spherical orthoschemes for various dihedral angles would be helpful.

I am a self studying enthusiast rather than a mathemetician and have taken no courses on this subject. A pointer to a comprehensive textbook would be perfect.