The crystal structure of alpha-K3AlF6 was solved and refined from a combination of powder X-ray and neutron diffraction data (a = 18.8385(3)angstrom, c = 33.9644(6)angstrom, S.G. l4(1)/a, Z = 80, R-P(X-ray) = 0.037, R-P(neutron) = 0.053). The crystal structure is of the A(2)BB'X-6 elpasolite type with the a = b approximate to a(e)root 5, c = 4a(e) superstructure (a(e), parameter of the elpasolite subcell) and rock-salt-type ordering of the K and Al cations over the B and B' positions, respectively. The remarkable feature of alpha-K3AlF6 is a rotation of 2/5 of the AlF6 octahedra by similar to pi/4 around one of the crystal axes of the elpasolite subcell, coinciding with the 4-fold symmetry axes of the AlF6 octahedra. The rotation of the AlF6 octahedra replaces the corner-sharing between the K and Al polyhedra by edge-sharing, resulting in an increase of coordination numbers of the K cations at the B positions up to 7 and 8. Due to significant deformations of the K polyhedra, the comer-sharing connectivity of the octahedral elpasolite framework is broken and the rotations of the AlF6 octahedra do not have a cooperative character. Elpasolites and double perovskites with similar structural organization are discussed. The difference in ionic radii of the B and B' cations as well as the tolerance factor are proposed to be the parameters governing the formation of elpasolites and double perovskites with broken comer-sharing connectivity of the octahedral framework.