Here is a dodecahedron made out of plastic pipes and nylon string. This sort of construction is called a "tensegrity", because it is held together by tension forces, as well as compression. This one was brought to me by an alien.

Notice the tying together of the previously triangular string arrangement in the centre. This cuts down on the number of tendons.

The sticks don't actually touch eachother. Here is a detail to show this..

Cafe de Mars.