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Polygonal Complexes and Graphs for Crystallographic Groups

  • Daniel Pellicer
  • Egon SchulteEmail author
Chapter
Part of the Fields Institute Communications book series (FIC, volume 70)

Abstract

The paper surveys highlights of the ongoing program to classify discrete polyhedral structures in Euclidean 3-space by distinguished transitivity properties of their symmetry groups, focussing in particular on various aspects of the classification of regular polygonal complexes, chiral polyhedra, and more generally, two-orbit polyhedra.

Keywords

Regular polyhedron Regular polytope Abstract polytope Complex Crystallographic group 

Subject Classifications

51M20 52B15 

Notes

Acknowledgements

We greatly appreciate the hospitality of the Fields Institute over extended periods of time during the Thematic Program on Discrete Geometry and Application in Fall 2011, and are very grateful for the support we have received. Daniel Pellicer was a postdoctoral fellow at Fields Institute in Fall 2011, and was also partially supported by PAPIIT–Mexico under grant IN106811-3 and CONACYT project 166951. Egon Schulte was also supported by NSF-grant DMS–0856675.

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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Centro de Ciencias MatematicasNational University of MexicoMoreliaMexico
  2. 2.Department of MathematicsNortheastern UniversityBostonUSA

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