"Hyper-Toast" was a math movie shown at HCSSiM.

The whole point of the movie was to show different views of hyperpolyhedra, such as the hypertetrahedron, hypercube, hyperoctagon, and the 24, 120, and 600 cell hyperpolyhdera, from here on refered to as Ned, Spot, and Bertha. There's no way I can do justice to this movie, since you really need to see hyperpolyhedra from all different angles in order to get an idea of what they really look like. It's worth seeing how one can make four dimensional objections come to life on a two dimensional screen.

By the way, these are the only regular hyperpolyhedra, just as the tetrahedron, cube, octahedron, dodecahedron, and icosahedron are the only regular polyhedra (known as the Platonic Solids). And just as in three dimensions, there is a constant relation between vertices, edges, and faces (Euler's formula `V-E+F=2`, there is a similar formula for hyperpolyhedra. See if you can figure out the four dimensional analog to Euler's formula from the table of cells, faces, edges, and vertices below.

h'tetra h'cube h'octa Ned Spot Bertha
C 5 8 16 24 120 600
F 10 24 32 96 720 1200
E 10 32 24 96 1200 720
V 5 16 8 24 600 120