Group theoretical analysis of 600-cell and 120-cell 4D polytopes with quaternions

Mehmet Koca*, Mudhahir Al-Ajmi, Ramazan Koç

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

11 Citations (Scopus)


600-cell {3, 3, 5} and 120-cell {5, 3, 3} four-dimensional dual polytopes relevant to quasicrystallography have been studied with the quaternionic representation of the Coxeter group W(H4). The maximal subgroups W(SU(5)):Z2 and W(H3) × Z2 of W(H 4) play important roles in the analysis of cell structures of the dual polytopes. In particular, the Weyl-Coxeter group W(SU(4)) is used to determine the tetrahedral cells of the polytope {3, 3, 5}, and the Coxeter group W(H3) is used for the dodecahedral cells of {5, 3, 3}. Using the Lie algebraic techniques in terms of quaternions, we explicitly construct cell structures forming the vertices of the 4D polytopes.

Original languageEnglish
Article number013
Pages (from-to)7633-7642
Number of pages10
JournalJournal of Physics A: Mathematical and Theoretical
Issue number27
Publication statusPublished - Jul 6 2007

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Modelling and Simulation
  • Mathematical Physics
  • Physics and Astronomy(all)


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