Compound of Five Tetrahedra
This polyhedron is created to look like 5 tetrahedron that pass through each other. In reality the center of this structure is hollow.
Begin by using the template below and cutting one face out of each color. You will need 5 colors, one for each of the apparent tetrahedra. In total you will be cutting 4 faces of each of the 5 colors.
Fold each piece along the fold lines and glue the bottom edges together to form a 3-sided pyramid with a ragged bottom edge. Mark one tab of each small pyramid with the noted asterick.
Take 5 of these small pyramids and glue them into a ring by connecting their tabs that contain the asterisks. You will now have a dimple made of 5 small pyramids.
Now you should be able to position the next round of pyramids into their correct positions by imagining where the next vertices of each tetrahedron will emerge.
The last pyramid piece to be glued into position can be very difficult. Father Mangus suggests in his book Polyhedron Models, to cement this part into position not as a pyramid. Once the part is secured into its place on the polyhedron you can secure the final edge of the pyramid.