Comments by "" (@TheDavidlloydjones) on "Perfect Shapes in Higher Dimensions - Numberphile" video.

  1. Why should higher dimensions be limited to 360 degrees? Why are we supposed to impose a three-dimensional ukase against "overlap" to higher dimensions? To take a simple example, a hypercube wraps around through, uh, "space," from our point of view. That looks like overlapping to me. OK, why then should the overlap by which all the polytopes with shallow angels overlap -- or maybe inter-lap in on themselves -- be disallowed? Put differently, what would we think of a Flatland mathematician objecting to almost all the polytopes in three dimensions because of the well-known Flatland "fact" that there are only two sides to an anything? (Or, alternately, they might think there are any number of edges, but no sides except in their imagination. But they can't imagine more than two sides, so all higher dimensions, in their opinions, would be limited to one hypertope, the free-floating sheet.)
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  2. It is perfectly natural that the Utah Teapot should be a Platonic form in computer science: this, after all, is the discipline which established that pepperoni is honorary vegetable.
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