Blender can create an icosahedron by adding an Icosphere with Subdivisions=1. You can then Subdivide it with 2 cuts to split each edge into thirds. Finally, dissolve the excess vertices and you are left with a geodesic sphere, and well on your way to that dome, soccer ball, Buckminsterfullerene, etc.
In more detail, for Blender 2.6:
- Shift-A | Mesh | Icosphere
- In the lower left, under Add Ico Sphere, set Subdivisions to 1.
- TAB for edit mode
- Mesh | Edges | Subdivide
- In the lower left, under Subdivide, set Number of Cuts to 2.
- Create the hexagons:
- Select the vertex in the center of any large, flat triangle.
- X | Dissolve Vertices
- Repeat for every large, flat triangle.
- Create the pentagons:
- Select the vertex at each of the points.
- X | Dissolve Vertices
- Repeat for every point.
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