• superspace formalism;
  • tungsten bronzes;
  • pentagonal tunnel homologous series;
  • modular structures

The large family of monophosphate tungsten bronzes with pentagonal tunnels (MPTBp), (PO2)4(WO3)2m with m ranging from 4 to 14, can be considered as modular structures via a description with (PO2)2(WO3)m modules related together by a symmetry operation and alternating along the z axis. Following the success of the application of the superspace for the description of the lillianites homologous series, a (3 + 1)-dimensional superspace model is efficiently defined to unify the structural analysis of the MPTBp. The (3 + 1)-dimensional model reveals hidden common characteristics such as the symmetry. An evaluation of the model for six well known members of the series was carried out from experimental data collected to this aim.