The following is a theorem of which I have great interest in but cannot find anything about on the internet,



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> Every 3-manifold of finite volume comes from identifying sides of some polyhedron
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I'm fairly certain that "identifying sides of some polyhedron" may be a simplification of the technical terminology. I believe it is just referring to gluing faces of polyhedron to form closed 3-manifolds. Such examples are given by the Seifert-Weber space, the Poincare homology sphere, the 3-dimensional real projective space, the $\frac{1}{2}$ twist cube space, etc. I'm assuming the proof is based off of [Moise's theorem](http://en.wikipedia.org/wiki/Moise%27s_theorem) and proceeds as follows,



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> Let $M$ be an arbitrary closed 3-manifold. By Moise's theorem we have that $M$ can be tetrahedralized, so we let $T$ be the tetrahedralization of $M$ consisting of tetrahedrons $t\_{1},...,t\_{n}$. Pick an arbitrary tetrahedra $t\_{1}$ of $T$ and proceed to glue $t\_{2}$ to $t\_{1}$, forming a new polyhedron $P\_{2}$, and then glue $t\_{3}$ to $P\_{2}$ resulting in $P\_{3}$, and so on. After all tetrahedra $t\_{1},...,t\_{n}$ have been glued, we have some resulting polyhedron $P\_{n}$. From here, then somehow show that $P\_{n}$ can be glued to $M$?
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Any references to papers, expository writing, a proof of, or even the formal statement and name of this theorem would be greatly appreciated!



3-manifold theorem reference request or proof
I think the reference that you are looking for is  [this article](http://arxiv.org/pdf/0806.1912)  by Cannon, Floyd, and Parry. 


