Grand antiprism and quaternions

Mehmet Koca*, Mudhahir Al Ajmi, Nazife Ozdes Koca

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)


Vertices of the four-dimensional (4D) semi-regular polytope, the grand antiprism and its symmetry group of order 400 are represented in terms of quaternions with unit norm. It follows from the icosian representation of the E 8 root system which decomposes into two copies of the root system of H 4. The symmetry of the grand antiprism is a maximal subgroup of the Coxeter group W(H 4). It is the group Aut(H 2 ⊕ H′ 2) which is constructed in terms of 20 quaternionic roots of the Coxeter diagram H 2 ⊕ H′ 2. The root system of H 4 represented by the binary icosahedral group I of order 120, constitutes the regular 4D polytope 600-cell. When its 20 quaternionic vertices corresponding to the roots of the diagram H 2 ⊕ H′ 2 are removed from the vertices of the 600-cell the remaining 100 quaternions constitute the vertices of the grand antiprism. We give a detailed analysis of the construction of the cells of the grand antiprism in terms of quaternions. The dual polytope of the grand antiprism has also been constructed.

Original languageEnglish
Article number495201
JournalJournal of Physics A: Mathematical and Theoretical
Issue number49
Publication statusPublished - 2009

ASJC Scopus subject areas

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


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