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This paper presents the first practical method for "origamizing” or obtaining the folding pattern that folds a single sheet of material into a given polyhedral surface without any cut. The basic idea is to tuck fold a planar paper to form a three-dimensional shape. The main contribution is to solve the inverse problem; the input is an arbitrary polyhedral surface and the output is the folding pattern. Our approach is to convert this problem into a problem of laying out the polygons of the surface on a planar paper by introducing the concept of tucking molecules. We investigate the equality and inequality conditions required for constructing a valid crease pattern. We propose an algorithm based on two-step mapping and edge splitting to solve these conditions. The two-step mapping precalculates linear equalities and separates them from other conditions. This allows an interactive manipulation of the crease pattern in the system …