Differences in the structure of water are investigated on the basis of a recent set of Monte Carlo simulations with a polarizable water model at temperatures corresponding to the same density below and above the density maximum. The simulations reproduced well the experimental differential pair correlation function of the molecular centers and its running coordination number. It is shown that with increasing temperature an increasing number of molecules leaves the tetrahedral hydrogen-bonded network. These interstitial molecules are located in the cavities of the tetrahedral network of the other molecules, forming closely packed structural units with their neighbours. The effect of the increasing number of these closely packed patches on the density of the system can compensate the increasing thermal motion of the molecules up to a certain point. These two opposite effects are shown to be responsible for the appearance of the density maximum of liquid water at 277 K.