There are continued attempts towards unifying the general circulation and cloud-resolving models. For designing high-resolution general circulation models, it is necessary to formulate a set of equations for the nonhydrostatic system such that when the the nonhydrostatic pressure is neglected, the system of equations reduce to a quasi-hydrostatic compressible model. Following the Konor and Arakawa (2009) approach, the governing equations of a unified model on icosahedral-hexagonal grid are formulated in the hybrid vertical coordinate. Further to this formulation, the flow dependent variables are represented in the basic equations into two parts - grid-resolved and a subgrid part - to formulated a system of equations that is capable of simulating the variability of unresolved processes. The advantage of splitting is obvious because the system of equations for grid-resolved variables are indeed those of a quasi-hydrostatic compressible model of the atmosphere. The discrete formulations of divergence, vorticity and gradient are then used to solve the shallow water model on the icosahedral-hexagonal grid as an example of the first stage development of a comprehensive unified model.