A 60-year-old problem with the atomic arrangements and exact compositions of alkali polytungstates related to hexagonal tungsten bronze (HTB) was solved. The systems A2WO4-WO3 (A = K, Rb) were restudied and the average monoclinic layered structures of stoichiometric polytungstates A4W11O35 (A = K, Rb, Cs, Tl) and A2W7O22 (A = K, Rb, Cs) were first successfully determined. The structures resemble those of "MoW11O36" and "MoW14O45" (J. Graham and A. D. Wadsley, Acta Crystallogr., 1961, 14, 379-383) and are derived from HTB by breaking into slabs parallel to (100) due to the ordered omission of some [WO]∞ chains along the hexagonal tunnels. The slabs in A4W11O35 (A = Cs, Tl) and A2W7O22 (A = Rb, Cs) are mutually shifted by the a/2 HTB unit cell axis. These data mainly confirmed our preliminary structural models of HTB-like alkali polytungstates (S. F. Solodovnikov, N. V. Ivannikova, Z. A. Solodovnikova and E. S. Zolotova, Inorg. Mater., 1998, 34, 845-853) and revealed a new similar thallium polytungstate. The structures of the HTB-like polytungstates and related compounds form a homologous series of layered complex oxides or fluorides An+2-xM3n+2X9n+8 where n = 2, 3 and 4 are equal to the numbers of HTB hexagonal tunnels across the polytungstate slab width for Tl2W4O13, A4W11O35 and A2W7O22 (A = K, Rb, Cs or Tl), respectively. The structures of the HTB-like polytungstates seem to intergrow with HTB-type AxWO3 to form, in particular, higher homologues of the series. Our group-supergroup analysis, measurements of nonlinear optical activity and electrical conductivity, and calculations of the bond-valence site energy barriers indicate possible ferroelectric/ferroelastic properties and moderate 2D oxide-ion mobility within the HTB-type slabs of the studied polytungstates.