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Torus Decompostions of Regular Polytopes in 4-space

In: Shaping Space

Author

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  • Thomas F. Banchoff

    (Brown University, Mathematics Department)

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.

Suggested Citation

  • Thomas F. Banchoff, 2013. "Torus Decompostions of Regular Polytopes in 4-space," Springer Books, in: Marjorie Senechal (ed.), Shaping Space, edition 127, chapter 20, pages 257-266, Springer.
    • Handle: RePEc:spr:sprchp:978-0-387-92714-5_20
    DOI: 10.1007/978-0-387-92714-5_20
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