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Determination of All Tessellation Polyhedra with Regular Polygonal Faces

  • Jin Akiyama
  • Takayasu Kuwata
  • Stefan Langerman
  • Kenji Okawa
  • Ikuro Sato
  • Geoffrey C. Shephard
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7033)

Abstract

A polyhedron (3-dimensional polytope) is defined as a tessellation polyhedron if it possesses a net of which congruent copies can be used to tile the plane. In this paper we determine all convex polyhedra with regular polygonal faces which are tessellation polyhedra.

Keywords

polyhedra nets tessellation Johnson-Zalgaller solids 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Jin Akiyama
    • 1
  • Takayasu Kuwata
    • 1
  • Stefan Langerman
    • 2
  • Kenji Okawa
    • 1
  • Ikuro Sato
    • 3
  • Geoffrey C. Shephard
    • 4
  1. 1.Tokai UniversityJapan
  2. 2.Université Libre de BruxellesBelgium
  3. 3.Miyagi Cancer CenterJapan
  4. 4.University of East AngliaUK

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