Crystal model for the closed topological vertex geometry

The topological string partition function for the neighbourhood of threespheres meeting at one point in a Calabi-Yau threefold, the so-called 'closedtopological vertex', is shown to be reproduced by a simple Calabi-Yau crystalmodel which counts plane partitions inside a cube of finite size. The model isderived from the topological vertex formalism. This derivation can beunderstood as 'moving off the strip' in the terminology of hep-th/0410174, andoffers a possibility to simplify topological vertex techniques to a broaderclass of Calabi-Yau geometries. To support this claim a flop transition of theclosed topological vertex is considered and the partition function of theresulting geometry is computed in agreement with general expectations.Comment: 26 pages, 7 figures; references added, classical part of flop analysis corrected and expande