We determine, in closed form, the flow profile corresponding to stationary, spherically symmetric, polytropic flow around a gravitating and radiating point mass. The profile is a branch of a quartic equation, relating distance to the central object to, for example, the local sound speed. Two branches of this equation are complex. The other two describe three different types of flow: subsonic and transonic accretion flow, transonic wind, and supersonic, super-Eddington flow. At any position in this flow, a supersonic regime may be linked to a subsonic one, through an adiabatic shock. Given the profiles, we determine the position of this shock, and vice versa. We also derive a stability criterion for the continuous and shocked flows.