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From: Archimedes Plutonium on 2 Feb 2010 02:35
So Wikipedia says this about the Poincare dodecahedral space:
--- quoting ---
The Poincaré homology sphere (also known as Poincaré dodecahedral
space) is a particular example of a homology sphere. Being a spherical
3-manifold, it is the only homology 3-sphere (besides the 3-sphere
itself) with a finite fundamental group. Its fundamental group is
known as the binary icosahedral group and has order 120.
--- end quoting ---

Much of this thread is about the distinction or precision definition
of finite versus
infinte number or line. So is it possible that in mathematics, they
never bothered to
precision define finite number but then again took time to give a
precision definition
of a fundamental group that is finite?

Can someone, dare to explain what a finite fundamental group versus a
infinite one?
Or would I be bending and fraying too many nerves as is, nerves that
are already on
edge.

Also, why not take any of the other regular polyhedra and announce
that they are a
finite-fundamental-group? Or what is it that they lack that they
cannot be such?

Archimedes Plutonium
www.iw.net/~a_plutonium
whole entire Universe is just one big atom
where dots of the electron-dot-cloud are galaxies
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