The Great Dodecahedron

The great dodecahedron is one of the Kepler-Poinsot polyhedra. Five pentagons meet at each vertex, but parts of the pentagons lie in the interior of the polyhedron and cannot be seen from the outside.

Question: The outer edges of the great dodecahedron are the edges of a Platonic solid. Can you figure out which one?

To build this model, first glue the 20 pairs of tabs where the three 108° angles meet. When doing so, be sure to fold "up" along the long-short dashed lines, as you will be making the 20 "dimples" of the great dodecahedron.

Once you have done this, continue so that five dimples meet at each vertex. Experienced model builders will see the relationship to the construction of the regular icosahedron.

• How to build a model.
• See Herman Serras's animations of the Kepler-Poinsot polyhedra.
• Steve Dutch enumerates the Kepler-Poinsot polyhedra.