Fig. 2.

Examples of covering maps $Y_N\to X$ for N = 5 with group of deck transformations ${\mathbb{Z}}_5$. (A) Euclidean case: a toroidal cluster covers a toroidal unit cell. (B) Hyperbolic case: a genus-6 cluster covers a genus-2 unit cell. In both cases, the red loops in Y_N are identified in the quotient $Y_N/{\mathbb{Z}}_5\cong X$.