3 geodesic spheres. composed by hexagons and pentagons.
Warning, these geospheres are made of ngons. So you need blender with Bmesh (blender 2.63 and upper)
I started from an icosahedron (from the Regular solid addon) Then I subdivised it the right number of times. (I don't remenber the values) And I dissolved the vertex in the hexagons and pentagons.
A picture is better than words, so : http://www.pasteall.org/pic/32230
Really neat but they would be a lot more useful if they had faces like in your preview image. I'm just getting edges and no faces.
I made it with blender 2.63a And the faces are Ngons.
Blender versions before Bmesh (merged since 2.63) doesn't support ngons. So it delete faces and keep only the edge.
You should use blender 2.63 and upper release.
nice how did you create these spheres I could ask ?:)