**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.