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We review three methods of counting abelian orbifolds of the form ℂ 3 /Γ which are toric Calabi‐Yau (CY). The methods include the use of 3‐tuples to define the action of Γ 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.

An introduction to counting orbifolds