Counting orbifolds

Abstract

We present several methods of counting the orbifolds C-D/Gamma correspondence between counting orbifold actions on 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 C-3, C-4, C-5, C-6 and C-7. Some remarks are made on closed form formulas for the partition function that counts distinct orbifold actions.