Three-periodic nets and tilings: regular and related infinite polyhedra

Acta Crystallographica. Section A, Foundations of Crystallography
Michael O'Keeffe

Abstract

The six infinite regular (flag-transitive) polyhedra with finite faces of Grünbaum and Dress are described as tilings of the P and D periodic minimal surfaces. The three polyhedra formed by analogous tiling of the G surface are also described. The nets of these polyhedra are identified. It is shown how these polyhedra, and the nets they carry, could be found by mining the EPINET database of structures. The nets of regular three-periodic polyhedra with infinite helical or zigzag faces are also identified.

Citations

Nov 26, 2008·Nature Materials·Scott M Woodley, Richard Catlow
Aug 1, 2018·Physical Chemistry Chemical Physics : PCCP·Menglei HuXi Zhu
Apr 17, 2009·Physical Chemistry Chemical Physics : PCCP·S M WoodleyC R A Catlow
May 13, 2014·Acta Crystallographica. Section A, Foundations and Advances·Egon Schulte
Feb 2, 2011·Physical Chemistry Chemical Physics : PCCP·Laurent A BaumesAvelino Corma
Mar 3, 2012·Angewandte Chemie·Scott M Woodley, Alexey A Sokol
Oct 18, 2013·Acta Crystallographica. Section A, Foundations of Crystallography·Olaf Delgado-FriedrichsDavide M Proserpio
Mar 16, 2021·Dalton Transactions : an International Journal of Inorganic Chemistry·Yan Yan LiXiao-Ping Zhou

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