Shaping Space pp 231-251 | Cite as

Convex Polyhedra, Dirichlet Tessellations, and Spider Webs

  • Walter Whiteley
  • Peter F. Ash
  • Ethan Bolker
  • Henry Crapo


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.


Planar Graph Voronoi Diagram Convex Polygon Convex Polyhedron Cell Decomposition 
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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Walter Whiteley
    • 1
  • Peter F. Ash
    • 2
  • Ethan Bolker
    • 3
  • Henry Crapo
    • 4
  1. 1.Mathematics and StatisticsYork UniversityTorontoCanada
  2. 2.Cambridge CollegeCambridgeUSA
  3. 3.Department of Mathematics and Computer ScienceUniversity of Massachusetts at BostonBostonUSA
  4. 4.Centre de recherche “Les Moutons matheux,”La VacquerieFrance

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