TITLE: Topological spaces made by identifying opposite faces of a cube?
QUESTION [20 upvotes]: My bashful, nameless, colleague asked me:
When you identify opposite faces of a square, then depending on where you twist or not, you get a torus, Klein bottle, or projective plane.

What spaces can you get when identifying opposite faces of a cube?

He was hoping for a reference.

REPLY [16 votes]: B. Everitt. 3-manifolds from platonic solids.  Topology and its applications, 2004. 

Covers everything you're asking for and more.