The Riemann surface for polylogarithms of half-integer index. which has the topology of an infinite dimensional hypercube. is studied in relation to one-dimensional KPZ universality in finite volume. Known exact results for fluctuations of the KPZ height with periodic boundaries are expressed in terms of meromorphic functions on this Riemann surface. https://www.bowlersparadisers.shop/product-category/6-ball-rollers/