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Ah, and I had assumed we were scalars! But you're right, and what's even better is that the icosahedron case generalizes to people walking on the surface of a
by pingswept 15y ago
Ah, and I had assumed we were scalars!
But you're right, and what's even better is that the icosahedron case generalizes to people walking on the surface of a sphere (assuming they're evenly spaced).
- Eliezer 15y agoErm, I could be wrong but wouldn't the icosahedron be the maximum "evenly spaced" set of people on the surface of a sphere (that weren't all confined to a great circle)? Lots of regular polygons, rather fewer regular polyhedra. (Of course if we make the jump to a 4D sphere we can put 600 people into the largest regular polytope, the hexacosichoron. http://en.wikipedia.org/wiki/Convex_regular_4-polytope http://en.wikipedia.org/wiki/Convex_regular_4-polytope) EDIT: I am wrong, it'd only take a uniform polyhedron, not a regular one. E.g. http://en.wikipedia.org/wiki/Icosidodecahedron http://en.wikipedia.org/wiki/Icosidodecahedron