Previous: Weird Multiplication
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
- 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