Perfect Shapes in Higher Dimensions - Numberphile
Carlo Sequin talks through platonic solids and regular polytopes in higher dimensions. More links & stuff in full description below ↓↓↓ Extra footage ...
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[PROF SEQUIN]: What do you make of this? 5, 6, 3, 3. What do you think comes next? [BRADY]: I'm gonna go... 7! [PROF SEQUIN]: 7. No, actually, it is another 3. Now you have a guess at what's 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 that's 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 let's start wit...
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[PROF SEQUIN]: What do you make of this? 5, 6, 3, 3. What do you think comes next? [BRADY]: I'm gonna go... 7! [PROF SEQUIN]: 7. No, actually, it is another 3. Now you have a guess at what's 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 that's 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 let's start wit...
