Making the Cut: Lattice Kirigami Rules
  In this paper we explore and develop a simple set of rules that apply to cutting, pasting, and folding honeycomb lattices. We consider origami-like structures that are extinsically flat away from zero-dimensional sources of Gaussian curvature and one-dimensional sources of mean curvature, and our cutting and pasting rules maintain the intrinsic bond lengths on both the lattice and its dual lattice. We find that a small set of rules is allowed providing a framework for exploring and building kirigami -- folding, cutting, and pasting the edges of paper. 
Toen Castle, Yigil Cho, Xingting Gong, Euiyeon Jung, Daniel M.   Sussman, Shu Yang, and Randall D. Kamien
cond-mat.soft cond-mat.mes-hall cond-mat.mtrl-sci