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Balloon polyhedra

By George Hart for the Museum of Mathematics

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For making mathematical models of polyhedra, a convenient and inexpensive material is the long clown balloon. This dodecahedron (made of ten balloons) and icosahedron (made of six balloons) are two examples from a study of Mathematical Balloon Twisting by Erik Demaine, Marty Demaine, and Vi Hart.

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At several Math Midway events, the Museum of Mathematics has been pleased to have a balloon polyhedron expert twist balloons into octahedra for the museum visitors. Here, Vi Hart is making an octahedron from one balloon.

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With practice, one can work up to more complex models, such as this cuboctahedron made from a single balloon. The balloon outlines the twenty four edges of a cuboctahedron, which consists of eight triangles and six squares.

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Even more spectacular is this “orderly tangle” of six concentric regular pentagons, made from six balloons. Detailed instructions to start you making mathematical balloon constructions are available here.

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