The 120-cell is a way of tiling the "3-sphere" with
120 dodecahedra. The mathematician Henri Poincaré considered
a space formed by one dodecahedron with its opposite pairs of
faces attached.
Is this also a 3-sphere?
No! It's called the Poincaré homology 3-sphere,
since it resembles the usual 3-sphere, but it's different: it contains
loops that you can't "pull tight". It contains
precisely 120 of them!
