alpha-AlF3 which adopts a rhombohedrally distorted form of the ReO3 structure at room temperature, undergoes a phase transition to the cubic ReO3 structure at 466 degreesC. The phase transition has been studied using molecular dynamics (MD) simulations performed with a polarizable ion model (PIM). The results are compared to information obtained from experimental diffraction data, and analogies to the tilting schemes of the structurally related perovskite phases are made. The cubic phase can be distinguished from the rhombohedral phase by following the Al-F-Al bond angles that describe the tilting of the AlF6 comer sharing octahedra as a function of temperature. The Al-F-Al chains are still bent in the so-called cubic phase, but the direction of tilting of the AlF6 octahedra varies continuously during the MD run, so that the time-averaged symmetry of the system is nearly cubic. The motion of the octahedra primarily involves a 360degrees rotation of the vector that describes the displacement of the F atom from its ideal position in a linear Al-F-Al chain. It is this 360degrees motion that distinguishes the cubic from the rhombohedral phase. The high-temperature phase is also associated with increased vibrations of the Al-F-Al chains. The results provide an explanation for the large thermal parameters observed experimentally for fluorine (in structures refined from diffraction data) above the phase transition. The simulation results suggest the possible existence of a third (orthorhombic) form of alpha-AlF3, which is energetically very similar to the rhombohedral phase at room temperature but differs in its octahedral tilting scheme.