Great Stellated Dodecahedron
Properties of the great stellated dodecahedron: Number of faces, edges and dihedral angle measure
(Be sure to check out the similarities between this and the small stellated dodecahedron!)
We can look at the great stellated dodecahedron in two different ways:
Just like the small stellated dodecahedron, the great stellated dodecahedron is simply 12 pentagrams intersected in a special way. They're just put together in a much tighter configuration in this polyhedron.
Look at the second picture and easily see the yellow pentagram. Can you find some of the others? You should be able to find pentagrams that are red, green, etc. Once again, like the small stellated dodecahedron, there are two pentagrams of each color. We can only see the ones facing us. There is another yellow pentagram on the other side that lies in a parallel plane to the one facing us! Just as before, this is true for all the other 6 colors.
When I constructed this model, I first built the icosahedron. Then I made the tips and glued them on. The stellated dodecahedron is made up of 20 tips with 3 isosceles triangles in each tips for a total of 60 triangles. Compare these numbers to those of the stellated dodecahedron. You'll really start to see why the dodecahedron and the icosahedron are duals!