Edge-Based Intersected Polyhedral Paper Sculptures Constructed by Interlocking Slitted Planar Pieces Jace Miller Computer Science Department Texas A&M University jacemiller84@gmail.com Ergun Akleman Visualization Department Texas A&M University ergun.akleman@gmail.com Abstract In this paper, we generalize George Hart’s slide-together sculptures as edge-based intersected polyhedral paper sculp- tures. Edge-based intersected polyhedra are also a conceptual generalization of Kepler’s Small Stellated Dodecahe- dron. These sculptures are constructed by interlocking slitted planar pieces without using glue. We present a simple procedure to construct slitted planar pieces for any given polyhedron. These sculptures can easily be constructed by children and can be used to teach properties of Platonic or Archimedean Solids through hands-on experience. 1 Introduction George Hart has developed a wide variety of interlocked planar pieces for construction of slide-together sculptures [2] and symmetric modular sculptures [3, 4]. We have observed that George Hart’s slide-together sculptures can be generalized and we have developed a procedure that allows people to construct their own slide-together sculptures (See Figure 1). These sculptures consist of a set of interlocked planar pieces (See Figure 2). The planar pieces are interlocked using slits. The resulting sculptures are stable and do not need glue. In our examples, the slitted planar pieces are cut from paper, but other materials such as sheet metal can also be used. The major advantage of our procedure is that it does not require any propriety software and it can easily be taught in a classroom. Our procedure generalizes slide-together sculptures. To generalize other modular sculptures of George Hart [3, 4], we believe that there is a need for software development. Figure 1: Our version of Small Stellated Dodecahedron that is constructed by interlocking slitted planar shapes shown in Figure 2. There are two parameters that define the shape of the edge-based intersected polyhedral paper sculptures: 1. Underlying polyhedral structure: The planar pieces are interlocked through the edge slits that are located in the edges of an underlying polyhedron. There are two conditions for underlying polyhedron to satisfy. • Planar Faces The faces of polyhedron have to be planar (or developable) since we use paper or sheet metal.