Grand antiprism and quaternions

Research output: Contribution to journalArticle

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Abstract

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
Volume42
Issue number49
DOIs
Publication statusPublished - 2009

Fingerprint

Antiprism
quaternions
Quaternion
apexes
Root System
Polytope
cells
diagrams
Cell
Diagram
Roots
symmetry
subgroups
norms
Maximal Subgroup
Coxeter Group
Symmetry Group
Binary
Norm
Symmetry

ASJC Scopus subject areas

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

Cite this

Grand antiprism and quaternions. / Koca, Mehmet; Al Ajmi, Mudhahir; Koca, Nazife Ozdes.

In: Journal of Physics A: Mathematical and Theoretical, Vol. 42, No. 49, 495201, 2009.

Research output: Contribution to journalArticle

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