Finite or periodic structures containing the cube motif can be synthesized and transformed into a variety of structures both at the theoretical and real, experimental level. The rhombellation topo-geometric operation may be used to transform the cube-shape into larger units and then build light (spongy) structures with larger voids. Hyper-clusters are polyhedral structures which nodes are polyhedral structures (the same or different ones). The paper presents some hypothetical spongy structures related to the cubic primitive pcu-net, with defects induced by cutting-off some atoms and/or bonds so that only corners are shared between two cubes. A diamondoid hyper-structure containing cube-coalesced corners was proposed for an eventual synthesis. The discussed structures are described in topological terms, particularly by sequential vertex connectivity and ring environment.
Keywords: cube; dia; diamondoid net; flu; pcu; spongy; topology.