Some Possible Final Projects

1. Create images of some five-dimensional (or higher) objects. In dimensions n higher than 4, there are just 3 platonic polyhedra, the n-dimensional cube, the n-dimensional simplex, and the n-dimensional octahedron.

2. Build 3-D models of some 4-D objects. You built a model of the hypercube. Consider also models of the 4-D simplex, the 4-D octahedron, the 24-cell, or various truncations of these objects.

3. Create images of the 4-D icosahedron. This may be an ambitious project, but I'd be glad to help you out.

4. Create images of the 4-D dodecahedron. Again, an ambitious project. I can help.

5. The two-dimensional plane can be divided up into a grid of squares, triangles or hexagons. Three dimensional space can be divided up into a grid of cubes, with 8 cubes at each corner. Such configurations are called "close packings." Investigate close-packing in 4-D. Do hypercubes close-pack? What about other 4-D Platonic polyhedra?

6. Read Flatland, by E. A. Abbot. Write a paper about this book.

7. Earlier this semester we discussed the idea of a dual of a 3-polyhedron. Write a paper describing the concept of a dual of a 4-D polyhedron. Illustrate this idea with pictures of 4-D objects and their duals.

8. Create images of various truncated 4-D platonic polyhedra.