  Lattice {\em Kirigami}, ultra-light metamaterials, poly-disperse aggregates,
ceramic nano-lattices, and two-dimensional (2-D) atomic materials share an
inherent structural discreteness, and their material properties evolve with
their shape. To exemplify the intimate relation among material properties and
the local geometry, we explore the properties of phosphorene --a new 2-D atomic
material-- in a conical structure, and document a decrease of the
semiconducting gap that is directly linked to its non-planar shape. This
geometrical effect occurs regardless of phosphorene allotrope considered, and
it provides a unique optical vehicle to single out local structural defects on
this 2-D material. We also classify other 2-D atomic materials in terms of
their crystalline unit cells, and propose means to obtain the local geometry
directly from their diverse two-dimensional structures while bypassing common
descriptions of shape that are based from a parametric continuum.
