The structure of Cs2AlF5 obtained by thermal dehydration of Cs2AlF5•H2O is determined ab initio from powder diffraction data, space group Pmn21, a = 6.36216 (17) Å, b = 12.7523 (4) Å, c = 11.4102 (3) Å, and Z = 6. Contrarily to most A2MF5 compounds presenting MF5
cis or trans-chains of corner-sharing MF6 octahedra, Cs2AlF5 is characterized by the rare occurrence of the face-sharing anion Al2F9
3− combined with an isolated AlF6
3− octahedron, the sum leading to Al3F15
6−. The structure of Cs3Al2F9 [space group P63/mmc, a = 6.2535 (2) Å, c = 14.7193 (6) Å, Z = 2] is confirmed to be isostructural with Cs3Fe2F9, built up from the same M2F9
3− dimers (M = Fe, Al). Both crystal structures are optimized by energy minimization density funtional theory (DFT) in the solid state using a hybrid PBE0 functional, and their relations with the hexagonal perovskites and elpasolites are discussed.