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Three-periodic nets and tilings: semiregular nets.

Olaf Delgado Friedrichs1, Michael O'Keeffe, Omar M Yaghi

  • 1Department of Chemistry, Arizona State University, Tempe, AZ 85287, USA.

Acta Crystallographica. Section A, Foundations of Crystallography
|October 29, 2003
PubMed
Summary

This study defines and describes fourteen new three-periodic semiregular nets and their tilings. These nets are important for understanding structures in crystal chemistry.

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Area of Science:

  • Crystallography
  • Materials Science
  • Geometry

Background:

  • Semiregular nets are fundamental structures in understanding crystal chemistry.
  • Previous work has cataloged regular and quasiregular nets.
  • A gap exists in the classification of specific types of semiregular nets.

Purpose of the Study:

  • To define and describe three-periodic semiregular nets.
  • To identify and enumerate nets beyond the known regular and quasiregular types.
  • To highlight the significance of these nets in crystal chemistry.

Main Methods:

  • Definition of three-periodic semiregular nets based on vertex and edge characteristics.
  • Systematic enumeration and description of fourteen distinct nets.
  • Analysis of associated natural tilings.

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Main Results:

  • Identification of fourteen novel three-periodic semiregular nets.
  • Detailed description of the geometric properties and tilings of these nets.
  • Demonstration of their relevance to crystal chemical structures.

Conclusions:

  • The fourteen newly described nets expand the known catalog of periodic nets.
  • These nets offer valuable models for diverse crystal structures.
  • Further exploration of these nets can advance crystal chemistry research.