  When flat or on a firm mechanical substrate, the atomic composition and
atomistic structure of two-dimensional crystals dictate their chemical,
electronic, optical, and mechanical properties. These properties change when
the two-dimensional and ideal crystal structure evolves into arbitrary shapes,
providing a direct and dramatic link among geometry and material properties due
to the larger structural flexibility when compared to bulk three-dimensional
materials. We describe methods to understand the local geometrical information
of two-dimensional conformal crystals quantitatively and directly from atomic
positions, even in the presence of atomistic defects. We then discuss direct
relations among the discrete geometry and chemically-relevant quantities
--mean-bond-lengths, hybridization angles and $\sigma-\pi$ hybridization. These
concepts are illustrated for carbon-based materials and ionic crystals. The
piramidalization angle turns out to be linearly proportional to the mean
curvature for relevant crystalline configurations. Discrete geometry provides
direct quantitative information on the potential chemistry of conformal
two-dimensional crystals.
