Making the Cut: Lattice Kirigami Rules

TL;DR

This paper develops a simple set of rules for cutting, pasting, and folding honeycomb lattices, enabling the systematic exploration and creation of kirigami structures with controlled curvature.

Contribution

It introduces a minimal rule set for lattice kirigami that preserves bond lengths and facilitates the design of complex origami-like structures.

Findings

A small set of rules allows for consistent lattice modifications.

Rules maintain intrinsic bond lengths on lattices and their duals.

Framework supports systematic kirigami design and exploration.

Abstract

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.