Abstract
It is a long-standing open problem to recognize whether every nonconvex polyhedron has a general unfolding algorithm. In the recent research, it is proposed grid-edge and grid-vertex unfolding algorithms to solve orthogonal polyhedron which is one class of nonconvex polyhedra. Since there are two fundamentals, the separated surface must have a refinement to be divided into n_1*n_2 grid and the orthogonal polyhedron is genus-zero. The aim of this thesis is to consider the unfolding algorithms run on the lattice polyhedra formed by unit cubes. The first research topic is the edge-unfolding algorithm for lattice Manhattan Towers. The main idea is to use many strips to flatten the faces of each layer and these strips are regarded as the bridge between two bands. The second research is to consider the edge-unfolding algorithm for one-layer lattice polyhedra with cubic holes. The principal concept is finding the connected bridge to link the holes and let the extending direction keep in rightward or upward direction. We propose the algorithms which are 1*1 edge-unfolding without refining grid size. It is also shown that there exists unfolding methods to flatten one-layer lattice polyhedra with genus >1 and monotone boundary.