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A sphere is not a convex polyhedron
by LostMyLogin 1y ago
A sphere is not a convex polyhedron
- guelo 1y agoAt the limit of faces they are.
- jibal 1y agoA sphere has no faces so it's not a convex poloyhedron.
- burnt-resistor 1y agoCorrection: a sphere has infinite faces so it's not an "convex poloyhedron [sic]." A convex polyhedron must have finite faces, so apeirotopes aren't allowed.
- jibal 1y agoA sphere has no faces, not "infinite" faces.
- teraflop 1y agoSure, and pi is the limit of a sequence of rational numbers, but lots of properties that hold for rational numbers don't hold for pi.
- guelo 1y agoAs you approach sphere you lose Rupertness.
- akoboldfrying 1y agoLimiting behaviour can be counterintuitive. As you add vertices to a polyhedron, some properties approach those of a sphere (volume, surface area), but others just get further and further away (number of surface discontinuities). It's not at all obvious which way "Rupertness" will go, or even whether it's monotone with respect to vertex addition.
- burnt-resistor 1y agoConvex polyhedra are required to be finite polytopes.