Shaping Space pp 257-266 | Cite as

Torus Decompostions of Regular Polytopes in 4-space

  • Thomas F. Banchoff


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.


Central Projection Torus Diagram Solid Torus Regular Polyhedron Regular Polytopes 
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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Mathematics DepartmentBrown UniversityProvidenceUSA

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