New Large Volume Solutions

In previous work, we have commenced the task of unpacking the $473,800,776$ reflexive polyhedra by Kreuzer and Skarke into a database of Calabi-Yau threefolds (see http://www.rossealtman.com). In this paper, following a pedagogical introduction, we present a new algorithm to isolate Swiss cheese solutions characterized by "holes," or small 4-cycles, descending from the toric divisors inherent to the original four dimensional reflexive polyhedra. Implementing these methods, we find $2,268$ explicit Swiss cheese manifolds, over half of which have $h^{1,1}=6$. Many of our solutions have multiple large cycles. Such Swiss cheese geometries facilitate moduli stabilization in string compactifications and provide flat directions for cosmological inflation.