We present several methods of counting the orbifolds $$ {{{{\mathbb{C}^D}}} \left/ {\Gamma } \right.} $$ . A correspondence between counting orbifold actions on $$ {\mathbb{C}^D} $$ , brane tilings, and toric diagrams in D - 1 dimensions is drawn. Barycentric coordinates and scaling mechanisms are introduced to characterize lattice simplices as toric diagrams. We count orbifolds of $$ {\mathbb{C}^3} $$ , $$ {\mathbb{C}^4} $$ , $$ {\mathbb{C}^5} $$ , $$ {\mathbb{C}^6} $$ and $$ {\mathbb{C}^7} $$ . Some remarks are made on closed form formulas for the partition function that counts distinct orbifold actions.