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[PROF SEQUIN]: What do you make of this? 5, 6, 3, 3. What do you think comes next? [BRADY]: Im gonna go 7! [PROF SEQUIN]: 7. No, actually, it is another 3. Now you have a guess at whats coming next. [BRADY]: 3. [PROF SEQUIN]: Good! Yes. As a matter of fact it continues to be 3, 3, 3. And you wonder, this is really a strange sequence, you know, what are we going to do with this? Well, this is the number of regular polytopes that exist in 3, 4, 5, 6, 7, 8, 9, and all higher dimensions. And thats what we are going to talk about today. Regular polytopes in N dimensions. A polytope is just a more general term that generalizes for 2-dimensional polygons, 3-dimensional polyhedra, and everything higher we call a regular polytope. That sounds a little scary, so lets start with something much simpler; the platonic solids. So here is a tetrahedron, that is the first platonic solid. Next we have a simple cube. Third one octahedron, made from eight equilateral triangles. Number four, twelv