12 verticess, 30 struts. 20 triangles, 12 pentagons. Dual to the dodecahedron. Very rigid. Click here to see a large icosahedron I made in France, using garden bamboo sticks instead of toothpicks. Click here to see an icosahedron that was rebuilt in Richmond Park. Geodesic domes are usually icosahedra with each triangular face divided into 4 ( or more ) triangles and bulged out to fit on a sphere.

This icosahedron has had ten sticks replaced with string, and a "diameter" of string added to give the whole thing stability. This model is particularly fun to loosen and then pull tight and see it kind of clicking into shape.