The unique geometrical features and structural potential of the centropolyindanes, a complete family of novel, 3D polycyclic aromatic hydrocarbons, are discussed with respect to the inherent orthogonality of their arene units. Thus, the largest member of the family, centrohexaindane, a topologically nonplanar hydrocarbon, is presented as a "Cartesian hexabenzene", because each of its six benzene units is stretched into one of the six directions of the Cartesian space. This feature is discussed on the basis of the X-ray crystal structures of centrohexaindane and two lower members of the centropolyindane family, viz. the parent tribenzotriquinacenes. Recent progress in multiple functionalization and extension of the indane wings of selected centropolyindanes is reported, including several highly efficient sixand eight-fold C-C cross-coupling reactions. Some particular centropolyindane derivatives are presented, such as the first twelve-fold functionalized centrohexaindane and a tribenzotriquinacene bearing three mutually orthogonal phenanthroline groupings at its molecular periphery. Challenges to further extend the arene peripheries of the tribenzotriquinacenes and fenestrindanes to give, eventually, graphite cuttings bearing a central bowl-or saddle-shaped center are outlined, as is the hypothetical generation of a "giant" nanocube consisting of eight covalently bound tribenzotriquinacene units. Along these lines, our recent discovery of a related, solid-state supramolecular cube, containing eight molecules of a particular tribromotrinitrotribenzotriquinacene of the same absolute configuration, is presented for the first time.