Geometrical property of the cluster model of the Yb–Cd icosahedral quasicrystal

Abstract

The geometrical property of an atomic structure model of the Yb–Cd icosahedral quasicrystal is discussed from the higher-dimensional viewpoint. An occupation domain for the framework that specifies the arrangement of the three building units of the structure is presented based on a specific archetype occupation domain for the cluster centres. Different cluster configurations are enumerated and the numerical values of their frequencies are given.

Keywords:

• icosahedral quasicrystals
• structure modelling
• higher-dimensional crystallography
• Yb–Cd