Regular and defective vertex configurations in icosahedral structures

S. I. Ben-Abraham, M. Baake, P. Kramer, M. Schlottmann

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


We have constructed all 5450 combinatorially possible vertex configurations formed by the Ammann rhombohedra. The defectiveness of the vertex configurations is quantified by a penalty functional defined as the minimal sum of squared distances between the dual acceptance domains for the constituent tiles of a given vertex. The vertices are then classified as ideal versus defective, quasiregular versus strictly forbidden, and regular versus singular. The classification is refined by defining rank as the dimension of the dual overlap and degree as the highest dimension of a facet violating the conditions of regularity.

Original languageEnglish
Pages (from-to)132-136
Number of pages5
JournalJournal of Non-Crystalline Solids
Issue numberC
StatePublished - 2 Feb 1993

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Ceramics and Composites
  • Condensed Matter Physics
  • Materials Chemistry


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