A Dodecahedron as a Cube with "Hats"

A dodecahedron shares eight of its vertices with a cube that can be nestled inside it. If you have a hard time picturing how a cube can fit inside a dodecahedron, make this model. You will create a cube and add a "hat" to each face to make a dodecahedron.

Steps

1. Cut out six copies of the smaller pattern piece and one copy of the larger one.
   
2. Fold and glue the pieces together to make six "hats" and one cube.
   
3. Tape the hats together on the underside of the pieces as shown.
   
4. Drape the hats over the cube to make a dodecahedron. I ran a marker over the edges of the hats to help show the resulting dodecahedron.
   

Notes

• The cube’s edges are a golden ratio times as long as the edges of the dodecahedron.