Origami techniques, as folding and unfolding, can be utilized in shrinkable structures. Especially when the crease pattern is rigid foldable, it can be treated as a mechanical linkage of rigid panels connected by hinges. Since rigid foldable crease patterns have the strong geometrical constraint of the facets not being able to stretch or bend, it is difficult to design new crease patterns, and variations of existing patterns are limited. However, it is known that there are cases where crease patterns can be made rigid foldable by adding some slits. This paper proposes a mechanical linkage that folds into a similar flat shape by adding slits. A method is presented of generating rigid foldable crease patterns in arbitrary polygons that fold smaller, and it is confirmed that structures that have a mechanism for shrinking can be generated from these crease patterns by using rigid thick panels and hinges.