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.
|دورية||Journal of Physics A: Mathematical and Theoretical|
|المعرِّفات الرقمية للأشياء|
|حالة النشر||Published - 2009|
ASJC Scopus subject areas