5
$\begingroup$

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.

Improve this question
$\endgroup$
1
  • $\begingroup$ After asking this question, I have had considerable success making these computations using methods of my own invention through 7-dimensional spherical space (spherical orthoschematic octotopes). The method involves iterated numerical integration in Excel spreadsheets. This is a work in progress as I'm working toward improved efficiency and accuracy. Interested parties can contact me at [email protected]. Thank you, Igor, for your advice and giving a darn. $\endgroup$
    – user32121
    Commented Mar 11, 2013 at 20:57

1 Answer 1

Reset to default
3
$\begingroup$

There is no software I am aware of. Nor is there any textbook. For hyperbolic orthoschemes (a very similar subject) you should check out Ruth Kellerhals' articles (there is a very detailed one in GAFA in 1995).

Improve this answer
$\endgroup$
2
  • $\begingroup$ There is no software? Is that definitive? Is there a resonably accessible paper? $\endgroup$
    – Jim Sather
    Commented Oct 23, 2012 at 16:18
  • $\begingroup$ Ruth's papers are accessible. As for software, I am pretty sure, though life is full of surprises. $\endgroup$
    – Igor Rivin
    Commented Nov 7, 2012 at 21:41

You must log in to answer this question.

Not the answer you're looking for? Browse other questions tagged .