  Monolithic structures can be built into graphene by the addition and
subsequent re-arrangement of carbon atoms. To this end, ad-dimers of carbon are
a particularly attractive building block because a number of emerging
technologies offer the promise of precisely placing them on carbon surfaces. In
concert with the more common Stone-Wales defect, repeating patterns can be
introduced to create as yet unrealized materials. The idea of building such
allotropes out of defects is new, and we demonstrate the technique by
constructing two-dimensional carbon allotropes known as haeckelite. We then
extend the idea to create a new class of membranic carbon allotropes that we
call \emph{dimerite}, composed exclusively of ad-dimer defects.
