  This paper considers "geometric" ideal triangulations of cusped hyperbolic
3-manifolds, i.e. decompositions into positive volume ideal hyperbolic
tetrahedra. We exhibit infinitely many geometric ideal triangulations of the
figure eight knot complement. As far as we know, this is the first construction
of infinitely many geometric triangulations of a cusped hyperbolic 3-manifold.
In contrast, our approach does not extend to the figure eight sister manifold,
and it is unknown if there are infinitely many geometric triangulations for
this manifold.
