I use the command hkcage to generate an icosahedral lattice on a sphere:

However, this only expands the strict icosahedral lattice (ie when using sphere=0) radially to match a spherical surface. As a result, the sizes of the hexagons and pentagons are not the same. The effect would be very dramatic if the parameter sphere is larger than 1. 

I am wondering if the code can be modified to generate a truly icosahedral lattice on a spherical surface, or if that piece of code is open to access?

Thank you and best regards,

Wei