The atomic-scale order of highly deformable yet chemically inert carbon frameworks animates a wide range of novel structural, optical, and electronic phenomena. For example, the division of surrounding space into two disconnected zones by an impenetrable suspended graphenic sheet enables adsorption of otherwise highly co-reactive species, such as alkali and halogen, in opposite subspaces, with an intense cross-sheet charge transfer that produces a new variant of ionic binding with a uncompensated electrostatic dipoles. New physics also results when the same species is adsorbed to both sides, with unusual "which-side" symmetry breaking at certain chemical potentials. New ways to induce gaps in graphene sheets can also be designed exploiting new stacking physics. In another example of geometry animated by nanoscale physics, mechanical manipulation of a carbon nanotube, followed by chemical functionalization, can split the tube into two independent channels whose extremely weak and tunable interaction generates a new energetic regime. Finally, the skewed orientation of the two weakly interacting adjacent layers of a folded graphene monolayer activates a new non-dispersive Raman band which is pinned to the wave-vectors of the periodic but incommensurate interlayer perturbing potential.