How can I build a model out of hexagons? (honeycomb effect) I am trying to build a dome that consists solely of hexagons.
They may vary a little in size but should retain their hexagonal shape and should not be squashed at the bottom.

Also, is there a way to make the hexagons a certain size?

Example of the model:


Desired effect (right half):



EDIT: 

I found out that what I'm asking for is a mathematical impossibility.
The shape I was going for is cald a Icosahedral Goldberg polyhedron.

As you can see the mathematical equation for faces by type is:
 12 {5} and 10(T − 1) {6} 
 T = m2 + mn + n2 = (m + n)2

Therefor it cannot exist.

My perception of the desired effect was false as this simply was a 2D tiled image.

What should I do with this question which I can not translate to a correct answer?
You could use "tissue" plugin to achieve similar result.

http://www.co-de-it.com/wordpress/code/blender-tissue

Use on icosphere for dome.