Calculations of water production rates and temperatures for rotating irregularly shaped bodies with and without topography are presented. These calculations are compared with the case of a spherical nucleus. For any combination of orbital parameters, rotation axis orientation, spin period, and physical properties of the nucleus (geometric albedo, emissivity, and thermodynamical properties) the heat diffusion equation in the surface normal direction is solved with the energy balance at the surface, which includes shadowing effects, as a boundary condition. This is done for all the cells in which the object is divided and for a complete orbital revolution around the Sun. Some of the main results obtained are: 1) Bodies with topographic features produce more water vapor than equal area spheres along most of their orbits; 2) Asymmetries in the behavior at pre and postperihelion are less pronounced than in the case of the sphere at large heliocentric distances; 3) Jet-like structures in the inner coma can result from topographic features; 4) Diurnal oscillations can be detectable away from perihelion, even for slightly irregular bodies.Peer reviewed