This study is concerned with the topography of nanostructures consisting of arrays of polycrystalline nanodots. Guided by transmission electron microscopy (TEM) measurements of crystalline Si (c-Si) nanodots that evolved from a "dewetting"process of an amorphous Si (a-Si) layer from a SiO2 coated substrate, we investigate appropriate formulations for the surface energy density and transitions of energy density states at grain boundaries. We introduce a new numerical minimization formulation that allows to account for adhesion energy from an underlying substrate. We demonstrate our approach first for the free standing case, where the solutions can be compared to well-known Wulff constructions, before we treat the general case for interfacial energy settings that support "partial wetting"and grain boundaries for the polycrystalline case. We then use our method to predict the morphologies of silicon nanodots. © 2014 AIP Publishing LLC.