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Icosahedral coincidence rotations

Published/Copyright: July 28, 2010
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Zeitschrift für Kristallographie - Crystalline Materials
From the journal Zeitschrift für Kristallographie - Crystalline Materials Volume 212 Issue 7

Abstract

The coincidence problem for three-dimensional discrete structures with icosahedral symmetry is reinvestigated. We present a parametric description of the coincidence rotations based on special quaternions, called icosian numbers. In particular, we give a characterization of the possible coincidence indices (Σ-factors) and present a complete list of the possible rotations with Σ < 50.

Published Online: 2010-7-28
Published in Print: 1997-7-1

© 2015 Oldenbourg Wissenschaftsverlag GmbH, Rosenheimer Str. 145, 81671 München

Articles in the same Issue

  1. Icosahedral coincidence rotations
  2. Localization and integration of diffraction spots from two-dimensional X-ray detector images by digital filtering
  3. Finite periodicity and crystal structures
  4. Structure determination from powder data using anomalous scattering: difference and partial, Patterson densities, and phases of structure factors
  5. Phase transitions of modulated Co-åkermanite, Ca2CoSi2O7
  6. Preparation and single crystal structure refinement of mixed orthophosphates M3Cr4(PO4)6 (M = Mg, Zn, Cu) – copper(II) in compressed octahedral coordination1
  7. Crystal structures of Ca5Ge3O11 and wollastonite-type GaGeO3
  8. One-dimensional staircase aggregates in crystals of 1,7-bis(dimethylamino)heptamethinium hexafluorophosphate, a polymethine dye
  9. Crystal structures of N-4-methyl phenyl)-2,2,2-trichloroacetamide, N-2,3-dimethyl phenyl)-2,2,2-trichloroacetamide and N-(2-nitro phenyl)-2,2,2-trichloroacetamide
  10. The structure of 6-(2-hydroxybenzylamino)purine acetic acid solvate
  11. Structural variations in the mercury(II) bis(1,1-dithiolate)s: the crystal and molecular structure of [Hg(S2CNMe2)2]
https://doi.org/10.1524/zkri.1997.212.7.473

Articles in the same Issue

  1. Icosahedral coincidence rotations
  2. Localization and integration of diffraction spots from two-dimensional X-ray detector images by digital filtering
  3. Finite periodicity and crystal structures
  4. Structure determination from powder data using anomalous scattering: difference and partial, Patterson densities, and phases of structure factors
  5. Phase transitions of modulated Co-åkermanite, Ca2CoSi2O7
  6. Preparation and single crystal structure refinement of mixed orthophosphates M3Cr4(PO4)6 (M = Mg, Zn, Cu) – copper(II) in compressed octahedral coordination1
  7. Crystal structures of Ca5Ge3O11 and wollastonite-type GaGeO3
  8. One-dimensional staircase aggregates in crystals of 1,7-bis(dimethylamino)heptamethinium hexafluorophosphate, a polymethine dye
  9. Crystal structures of N-4-methyl phenyl)-2,2,2-trichloroacetamide, N-2,3-dimethyl phenyl)-2,2,2-trichloroacetamide and N-(2-nitro phenyl)-2,2,2-trichloroacetamide
  10. The structure of 6-(2-hydroxybenzylamino)purine acetic acid solvate
  11. Structural variations in the mercury(II) bis(1,1-dithiolate)s: the crystal and molecular structure of [Hg(S2CNMe2)2]
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