  We review three methods of counting abelian orbifolds of the form C^3/Gamma
which are toric Calabi-Yau (CY). The methods include the use of 3-tuples to
define the action of Gamma on C^3, the counting of triangular toric diagrams
and the construction of hexagonal brane tilings. A formula for the partition
function that counts these orbifolds is given. Extensions to higher dimensional
orbifolds are briefly discussed.
