It seems intuitively clear that the sphere can be approximated (both in surface area, but also in a more geometric sense) by certain classes of polyhedra. Do there exist any good formalizations of this notion? Is there a simple sequence of polyhedra which "converge" to the sphere? Does anyone know of a good reference on this subject?
2026-03-26 19:18:58.1774552738
In what sense is the sphere the limit of convex polyhedra?
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A geodesic polyhedron is a candidate. Mathematica has a built-in function
GeodesicPolyhedron[n]. Here is $n=12$: