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With the advent of affordable three-dimensional printing and fabrication devices, the design of 3D objects has become an increasingly central activity in creative computational work. A recurring issue in this sort of design, however, is overcoming the "two-dimensional bottleneck" of the standard computer screen and associated conventional input devices: that is, it is difficult to create and visualize tangible objects using such hardware combination and (generally complex) modeling software. As a consequence, there is a growing need for a variety of innovative 3D input tools and techniques that allow users to create, customize, and visualize spatial objects and information "by hand". This paper describes a working example of such a tool: a tangible 3D sketching tool called Easigami, which permits users to assemble a wide variety of polyhedral objects by connecting and folding polygonal pieces. The physical arrangement of Easigami pieces is read into a computer and displayed interactively, in real time. Thus Easigami, by its design, blends the natural physical ability of folding paper-like materials with the power of computational representation. This paper describes the design of Easigami, presents a scenario of its use, and outlines ongoing and planned future work of the system.