  We investigate Farley's CAT(0) cubical model for Thompson's group F (we adopt
the classical language of F, using binary trees and piecewise linear maps).
Main results include: in general, Thompson's group elements are parabolic; we
find simple, exact formulas for the CAT(0) translation lengths, in particular
the elements of F are ballistic and uniformly bounded away from zero; there
exist flats of any dimension and we construct explicitly many of them; we
reveal large regions in the Tits Boundary, for example the positive part of a
non-separable Hilbert sphere, but also more complicated objects. En route, we
solve several open problems proposed in Farley's papers.
