A deltahedron is a convex polyhedron, each of whose faces is an equilateral triangle. Each pair of adjacent triangles must ``bend outward'' (not be coplanar or bend inward).

- Try to construct all of the deltahedra and draw a good sketch of each one.
- How many of the deltahedra have an odd number of faces? An even number of faces? Find a proof for what you observe.
- Assume that each triangle has a side length of 1 unit.
Determine the volumes of the following deltahedra:
- Tetrahedron (4 triangles).
- Octahedron (8 triangles).
- The deltahedron with 10 triangles.
- The deltahedron with 14 triangles.

- You can fit 4 tetrahedra around an
octahedron to make a larger tetrahedron.
- Make a sketch to illustrate this.
- What is the relationship of the volume of the large tetrahedron to the volume of one of the small tetrahedra?
- Use this information to determine a relationship between the volume of the octahedron and one of the small tetrahedra.

Wed Apr 21 08:26:07 EDT 1999