The movie of the book.
The Fifty-Nine Icosahedra by H.S.M.Coxeter,P.Du Val, H.T.Flather,J.F.Petrie.
Select a Stellation by clicking on a radio button.
You might need to click on the applet to start it. If you resize the page do a refresh. An explanation of the other controls is at the bottom of the page.
For an understanding of the topic visit some of the links.
Steven Dutch's Stellations of the Icosahedron
Bulatov, V. "Stellations of Icosahedron."
R. Maeder's "Stellated Icosahedra"
George Hart's 59 Stellations of the Icosahedron does similar things in glorious VRML
Weisstein, Eric W. "Icosahedron Stellations." From MathWorld--A Wolfram Web Resource.