Initial ideas - when I thought that any collection of triangles in a roughly spherical shape was a geodesic dome (all links are to Cabri 3D files)
1. Simple dome
2. More complicated: dome 2 dome 3 dome 4
3. A variation, just for fun
Correction: the vertices of triangles ought to lie along geodesics
1. The problem (the geodesics do not intersect nicely in one point)
2. Greatcircles on a dodecahedron (collections of triangles formed from intersections would form geodesic domes - but not very practicable ones!)
Brief details of how to make sense of a file are contained in this Word document, or click here for a Flash demo (related file moving_Claude1.cg3) giving further details.