Related Experiment Video
Updated: Jul 22, 2026

Construction and Systematical Symmetric Studies of a Series of Supramolecular Clusters with Binary or Ternary Ammonium Triphenylacetates
Published on: February 15, 2016
Indexing approximants of icosahedral quasicrystals
1CECM/CNRS, 15 rue Georges Urbain, F-94407 Vitry CEDEX, France.
Abstract:
It is well known that the crystallography of approxi-mants is directly related to that of the parent quasicrystal, once its unit-cell vectors are identified as parallel projections of certain N-dimensional lattice nodes A(i). Derived here are explicit simple relations for calculating the shear matrices varepsilon and the related crystallographic properties of the corresponding approximants, including diffraction indexing and the determination of the lattice in perpendicular space. Applied to low-dimensional approximants, the derivation shows that the systematic 'accidental' extinction rules observed in the pentagonal phases are generic extinctions that are due to the geometrical properties of the projected 1D lattice and are independent of the actual model of the quasicrystal.
Related Concept Videos
Structures of Solids
Crystal Field Theory - Octahedral Complexes
To explain the observed behavior of transition metal complexes (such as colors), a model involving electrostatic interactions between the electrons from the ligands and the electrons in the unhybridized d orbitals of the central metal atom has been developed. This electrostatic model is crystal field theory (CFT). It helps to understand, interpret, and predict the colors, magnetic behavior, and some structures of coordination compounds of transition metals.
CFT focuses on...
The Seven Crystal Systems: Overview
Crystallographic Point Groups
Law of Rational Indices
Imperfections in Crystal Structure: Stoichiometric Point Defects

