  In the same way that a contact manifold determines and is determined by a
symplectic cone, a Sasaki manifold determines and is determined by a suitable
Kahler cone. Kahler-Sasaki geometry is the geometry of these cones.
  This paper presents a symplectic action-angle coordinates approach to toric
Kahler geometry and how it was recently generalized, by Burns-Guillemin-Lerman
and Martelli-Sparks-Yau, to toric Kahler-Sasaki geometry. It also describes, as
an application, how this approach can be used to relate a recent new family of
Sasaki-Einstein metrics constructed by Gauntlett-Martelli-Sparks-Waldram in
2004, to an old family of extremal Kahler metrics constructed by Calabi in
1982.
