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Abstract
When a regular polyhedron in ordinary 3-space is inscribed in a sphere, then a decomposition of the sphere into bands perpendicular to an axis of symmetry of the polyhedron determines a corresponding decomposition of the polyhedron. For example, a cube with two horizontal faces can be described as a union of two horizontal squares and a band of four vertical squares, and an octahedron with a horizontal face is a union of two horizontal triangles and a band formed by the six remaining triangles.
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Mathematics Department, Brown University, Royce Family Professor in Teaching Excellence 2005-8, Providence, RI, 02912, USA
Thomas F. Banchoff
- Thomas F. Banchoff
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Correspondence toThomas F. Banchoff.
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Dept. Mathematics & Statistics, Smith College, College Lane 44, Northampton, 01063, Massachusetts, USA
Marjorie Senechal
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© 2013 Springer Science+Business Media New York
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Banchoff, T.F. (2013). Torus Decompostions of Regular Polytopes in 4-space. In: Senechal, M. (eds) Shaping Space. Springer, New York, NY. https://doi.org/10.1007/978-0-387-92714-5_20
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