Geometry:what is the opposite of a sphere?& what shape maximises surface area/volume?

[ijabbott]

(02-17-2019 05:10 PM)StephenG1CMZ Wrote:  Right now I'm no longer certain that a sphere could have an infinite number of faces, or whether the maximum number of faces has any relevance to spheres. But I am sure someone here can explain.

One thing you can be sure of is that it will satisfy the Euler characteristic for a polyhedron: F + V = E + 2. For tessellating a sphere, the simplest case is one face and one vertex, but no edges.