Counting Orbifolds

Understand

We present several methods of counting the orbifolds C^D/Gamma.

• A 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.