Originally Posted by

**johnbarkwith** I can use hyperspherical coordinates to express a,b,c,d in 3 variables as follows:

a=cosF

b=cosG sinH sinF

c=sinG sinH sinF

d=cosH sinF

This means that the manifold has dimension 3. I have read that I will need atleast 2 charts to cover the whole manifold, however wont the chart mapping (F,G,H) to (Z=a+ib , W=c+id)

(-W* , Z* )

cover the whole manifold? If not can you please show me the two charts needed? Thankyou very much for your help, this problem has been bugging me for weeks now..