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?
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.