The four-connected three-dimensional (3D) nets obtained by sharing the vertices, edges and faces of the 1,3-stellated cube (called the bru polyhedral unit) were enumerated by Alberti [Am. Mineral. (1979), 64, 1188 1198]. This enumeration has been reexamined and the topological properties of the simpler nets have been determined. Among the 45 selected 3D nets, there are seven polyhedral subunits. eight three-connected two-dimensional (2D) nets and 16 types of one-dimensional (ID) subunit including chains, columns and tubes. Only four nets are represented by actual materials: brewsterite, heulandite, scapolite and stilbite. The only common subunit to these four nets is bru. Two nets, including scapolite, have tetragonal symmetry. Ten out of 45 3D nets were chosen for distance-least-squares refinement to obtain refined coordinates of T atoms and cell dimensions. This type of topological analysis provides useful information for the classification of framework structures. The concepts used here arc yielding many additional 3D nets from other polyhedral units.
