faceted dome

Hey everyone. 

i am having major problems coming up with a system for constructing a dome. 

Im essentially trying to create a dome out of one module. The module should have the same dimensions regardless of its location in the dome. I looked into dividing a sphere into points which are at equal distance from each other, however, this seems to be an impossible task. I was initially looking into a geodesic dome, however, the problem with that is that the hexagons which make up the dome start to distort and the higher the frequency of the dome the more variations there of that hexagon. What i am trying to find out now is if it is possible that the form of the dome is governed by the module instead of the dome being subdivided into smaller modules. This basically mean that the dome no longer needs to be confined to the shape of a half sphere. it could even turn into a flatter dome or a more parabolic dome as long as the module remains constant. I have no idea if this is even possible but if someone has any idea of how and if this can be achieved their advice would be greatly appreciated. The module also doesn't have to remain a hexagon it could be octagonal as long as it works.  

Thanks 

Faraz