between up- and downflows is present in idealized hexagonal convection cells that have been used in analytical studies of convection and supergranulation in particular [e.g., @Chandrasekhar1961; @Gough1975; @Busse2007]. These hexagonal cells are characterized by a central upflow region surrounded by a network of downflows [@Chandrasekhar1961; @Toomre1977; @Busse2003], similar to supergranulation. The opposite case of strong downflows surrounded by a weaker network of upflows was also considered [@Busse2004; @Busse2007]. For example, theoretical attempts to explain the phase velocity of supergranulation and its contribution to maintaining the near-surface shear layer [@Busse2004; @Busse2007] are based on decomposing the solution to the Navier-Stokes equations in terms of planforms that are constructed from such patterns in the horizontal direction.

The main aim of our work is to provide a statistical characterization of the spatial pattern of supergranulation beyond the power spectrum. In other words, we want to find out whether convective patterns, such as hexagons, can be directly related to the supergranulation data. Additionally, our longer-term aim is to construct synthetic supergranular flow fields. The availability of synthetic flow fields could be useful in helioseismic methods for studying subsurface convection [e.g., @Hanasoge2012; @Duvall2014].

Information on the skewness is contained in the bispectrum, which is a 