You can inscribe a tetrahedron in a dodecahedron. If you inscribe five, one at each vertex of the topmost face, you create a beautiful solid.
Cut out 20 copies of the shape from the pattern. If you would like to make each tetrahedron a unique color, cut four template pieces out of each color.
Fold and glue the pieces to form the 20 vertices.
Tape five vertices together as shown. Place the tape on the inside of the model. Use one vertex of each color if you are making a multi-color model.
Continue taping vertices onto the model, placing the tape on the inside.
Richard Otis created this model using a different color for each tetrahedron. This helps you visualize how the tetrahedra are arranged.
The shape of each face can be constructed as shown.
There two different ways you can inscribe a tetrahedron in a dodecahedron that are mirror images of each other so you can create two different versions of this model—a left-handed version and right-handed one. The pieces themselves are mirror images of each other as well so you can simply replace valley folds with mountain folds (effectively turning each part inside out) to make the mirror image version.