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Yeah--they aren't spheres. Some are oblate spheroids, more or less, and most have depressed areas on top and bottom.... Say, what is the equation for a pumpkin shape anyway?

x^2 + y^2 + z^2 = 16 + cos[4pi * arctan(x/y)]

(From http://blog.wolfram.com/2010/10/29/scary-mathematica-movies-for-halloween/ )

I'm not sure of a pumpkin's equation, but it probably has something to do with pie.

damm you foobar!! you stole the pie!

Does it matter how many pieces we divide the pie into?

Depends.

It doesn't matter, a pumpkin is homeomorphic to a sphere.

assuming there isn't a giant hole in it, or if it doesn't cave back into itself

Wait. Faces can go on non-spheres as well! Wow. Evil.

A cube is homeomorphic to a sphere, and a cube has faces... so homeomorphism does not apply.

You can paint a face on a wall, and that is a plane fact.

Made me laugh.