This shape consists of 60 struts. You can think of it as any of the following:

• 12 Pentagons touching each other at the corners ( compare to a dodecahedron which is 12 pentagons sharing sides )
• 20 triangles connecting to each other at the corners ( compare to an icosahedron which is 20 triangles touching sides ).
• A dodecahedron whose corners have been shaved off ( where the triangles are )
• An icosahedron whose corners have been shaved off ( where the pentagons are )
• 6 regular Decagons ( 10 sided polygon ) arranged evenly around a sphere.

This model shows how an icosidodecahedron is related to a dodecahedron. In this case the dodecahedron is formed by the CDs, and the icosidodecahedron is formed by the yellow strings holding them together/apart. Zorro is keeping an eye out for any lurking baddies.

As this shape isnt naturally rigid, the model in the next set of pictures is tensioned with nylon threads to form 5 cornered stars in each pentagon. This makes it wonderfully strong and bouncy.

The struts form 6 geodesic decagons around the object, and the nylon threads keeping the tension form 10 geodesic hexagons ! 6*10=60, 10*6=60. Geodesic = shortest distance between points on the sphere. ie great circles or equators.

Bet you've never seen an icosahedron sitting on a park bench. This picture is actually looking straight down one of the "poles", so the star shape in the middle is actually the backside.

Being based on the pentagon, this structure is replete with golden rectangles, which may be another factor explaining its elegance. For instance, in the picture on the left, the central "envelope" shape is a golden rectangle. In the background of this picture you can see a "tensegrity" dodecahedron, which you can also look at as an icosidodecahedron.