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Convex Polyhedra, Dirichlet Tessellations, and Spider Webs

In: Shaping Space

Author

Listed:
  • Walter Whiteley

    (York University, Mathematics and Statistics)

  • Peter F. Ash

    (Cambridge College)

  • Ethan Bolker

    (University of Massachusetts at Boston, Department of Mathematics and Computer Science)

  • Henry Crapo

    (Centre de recherche “Les Moutons matheux,”)

Abstract

Plane pictures of three-dimensional convex polyhedra, plane sections of three-dimensional Dirichlet tessellations, and flat spider webs with tension in all the threads are essentially the same geometric object. At the root of this remarkable coincidence is a single geometric diagram that permits us to offer a unified image of the connections among these and other objects. Some hints of these connections are more than a century old, but others are very recent. We begin with an historical sketch.

Suggested Citation

  • Walter Whiteley & Peter F. Ash & Ethan Bolker & Henry Crapo, 2013. "Convex Polyhedra, Dirichlet Tessellations, and Spider Webs," Springer Books, in: Marjorie Senechal (ed.), Shaping Space, edition 127, chapter 18, pages 231-251, Springer.
    • Handle: RePEc:spr:sprchp:978-0-387-92714-5_18
    DOI: 10.1007/978-0-387-92714-5_18
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