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Shaping Space pp 257-266 | Cite as

Torus Decompostions of Regular Polytopes in 4-space

  • Thomas F. Banchoff
Chapter

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.

Keywords

Central Projection Torus Diagram Solid Torus Regular Polyhedron Regular Polytopes 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Mathematics DepartmentBrown UniversityProvidenceUSA

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