Icosidodecahedron

Six wire loops can be combined to make a projection of an icosidodecahedron onto a sphere.

http://en.wikipedia.org/wiki/File:Icosidodecahedron.png

 
I've been playing with a simple way to approximate a sphere with the least copper wire and the smallest gaps in between for some possible future electrostatic plasma experiments.  Of the platonic solids the best sphere approximations are the dodecahedron and icosahedron.  However, the icosahedron has five edges that meet at each corner, which seems like a waste of wire in a dense area.  Ultimately, I think the best approximation will be a « soccer ball » truncated icosahedron; however, that can not be made with simple loops of wire.  This pattern, the icosidodecahedron, is interesting; it combines an icosahedron and dodecahedron together.  If you dropped out the five sided faces and pushed everything together it would be a icosahedron; if you dropped the three sided faces and put the rest together it would be a dodecahedron.  By combining the 20 sides of an icosahedron and 12 sides of a dodecahedron we get an archimedian solid, the icosidodecahedron.