  The concept of kirigami has been extensively utilized to design deployable
structures and reconfigurable metamaterials. Despite heuristic utilization of
classical kirigami patterns, the gap between complex kirigami tessellations and
systematic design principles still needs to be filled. In this paper, we
develop a unified design method for deployable quadrilateral kirigami
tessellations perforated on flat sheets with different topologies. This method
is based on the parametrization of kirigami patterns formulated as the solution
of a linear equation system. The geometric constraints for the deployability of
parametrized cutting patterns are given by a unified theorem covering different
topologies of the flat sheets. As an application, we employ the design method
to achieve desired shapes along the deployment path of kirigami tessellations,
while preserving the topological characteristics of the flat sheets. Our
approach introduces interesting perspectives for the topological design of
kirigami-inspired structures and metamaterials.
