Hyper Toast

"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

First, you need a piece of hyperbread. Take two loaves of bread and connecting them at their vertices. For a secure bond, I recommend peanut butter (the creamy kind). The resulting hyperloaf will be bigger than a breadbox, but simultaneously smaller.

Now, simply slice off a topologically equivalent but smaller volume from your hyperloaf. If you want to make large amounts of hypertoast you should consider taking your loaf to the local baker and asking to use their slicing machine, since repeatedly twisting a knife through the fourth dimension can lead to wrist strain and RSI.

Toasting your hyperbread is somewhat difficult because most toasters exist in only three dimensions. You will have to toast one cross-section at a time. Each section of hypertoast will resemble a piece of toast, but they will have infinitely small fourth-dimensional volume (analogous to a square created when a cube crosses through a plane). You might think, then, that your hypertoast would never be finished. But since an infinitely thin volume of bread requires an infinitely small amount of time to toast, you can just push your bread through and be done! In fact, you'll have to carefully adjust the heat settings to make sure it doesn't burn.

Theoretical explorations of hyperbread often use very thin breads that don't extend much into the fourth dimension, in order to simplify the calculations. A seminal work in this field is the allegorical textbook-novel flatbreadland.