I don’t know how Wolfram Alpha knows; I’m fearfully ignorant of this sort of thing myself. Perhaps there’s a well-known decomposition of the 600-cell into nice simple bits whose 4-volume is easy to calculate?
The method I use below (integrate its surface area) works for every regular polytope, so it could be the method Wolfram Alpha uses. The only difficult part is simplification of a complicated trigonometric expression, but Wolfram Alpha eats those for breakfast.
On the other hand there are only three families of regular polytope above dimension 4, so maybe it just knows a general formula for those three families and then just has the five exceptional regular polytopes programmed in as special cases.
This was quick, if true.
How does Wolfram Alpha knows that? And since when?
http://hi.gher.space/wiki/Hydrochoron
Those guys should update, and also should Wikipedia.
I don’t know how Wolfram Alpha knows; I’m fearfully ignorant of this sort of thing myself. Perhaps there’s a well-known decomposition of the 600-cell into nice simple bits whose 4-volume is easy to calculate?
The method I use below (integrate its surface area) works for every regular polytope, so it could be the method Wolfram Alpha uses. The only difficult part is simplification of a complicated trigonometric expression, but Wolfram Alpha eats those for breakfast.
On the other hand there are only three families of regular polytope above dimension 4, so maybe it just knows a general formula for those three families and then just has the five exceptional regular polytopes programmed in as special cases.
The second of those seems extremely likely. (But, I repeat, I don’t really know anything about this stuff.)