How can I build a looking-like sphere using triangles?
For those of you who played D&D, I mean the 20 faced dice, for example.

All triangles that build the sphere must be all equal in their area, and all of their angles are 60 degrees.
An image would explain better:

Moderators: I have devastatedly compressed the image to 7.5 kb,
I hope you don't mind that I have included a file.