Exploring 3D space with a computer - Part 2: a set of solids
Adrian Oldknow
Dodecahedron
We start with building a dodecahedron with a face defined by two points in the ground plane. We can then create two straight lines joining adjacent vertices on a face, and find their intersection point. This defines the vertex of one of the pentagonal pyramids we need to `glue' onto the dodecahedron. Create a polygon covering the desired face and then use the `Pyramid' tool to create the pentagonal pyramid defined by this polygon and the new vertex point. In order to create similar pyramidal stellations, we can reflect our first one in one of the planes of symmetry of the dodecahedron. We can also use rotation about an axis of symmetry as shown.
Continuing in this way we can build all twelve pentagonal pyramids to complete the lesser stellated dodecadron.
You can download the files 
Stellation.cg3, Stellation two.cg3 and Stellated.cg3.
Can you use Cabri 3D to build other stellations based on the regular polyhedra?
A copy of Cundy and Rollett's `Mathematical Models' (Tarquin) might be a good read at this point!
http://www.amazon.co.uk/exec/obidos/ASIN/0906212200/202-2214395-3179831
Here's our model for you to play with!
