So the dodecahedron and the icosahedron are dual solids. The icosahedron has 20 faces and 12 vertices, while the dodecahedron has 12 faces and 20 vertices. It means that if you truncate either one of them to the same point, you send up with the same shape - the icosidodecahedron.

I made the paper solid from a net from korthalsaltes.com..

And I made the paper geodesic version from Vince Matsko.. (If using his nets, you will need three pages of the pentagons, and one page of the triangles. The tabs for the five triangles making up each pentagon will go in the middle. The triangle is equilateral so doesn't matter where you put the tab).

Here's the two of them together..

## Sylvia Johnson

My mind boggles at all the time, effort and calculations that went into making those balls. I think you must have got those skills from Dad because it is all beyond me. Congratulations! I had to laugh at the photo of you with a ball on your head.