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4D pyritohedral symmetry
Other Title(s)
تماثل متعدد الأوجه ذو التركيب المشتبه لمعدن البايريت في الفضاء الاقليدي ذو الأبعاد الأربعة
Joint Authors
Koca, Nazifah O.
al-Qannubi, Amal J. H.
Koca, Muhammad
Source
Sultan Qaboos University Journal for Science
Issue
Vol. 21, Issue 2 (31 Dec. 2016), pp.151-162, 12 p.
Publisher
Sultan Qaboos University College of Science
Publication Date
2016-12-31
Country of Publication
Oman
No. of Pages
12
Main Subjects
Abstract EN
We describe an extension of the pyritohedral symmetry in 3D to 4-dimensional Euclidean space and construct the group elements of the 4D pyritohedral group of order 576 in terms of quaternions.
It turns out that it is a maximal subgroup of both the rank-4 Coxeter groups W (F4) and W (H4), implying that it is a group relevant to the crystallographic as well as quasicrystallographic structures in 4-dimensions.
We derive the vertices of the 24 pseudoicosahedra, 24 tetrahedra and the 96 triangular pyramids forming the facets of the pseudo snub 24- cell.
It turns out that the relevant lattice is the root lattice of W (D4).
The vertices of the dual polytope of the pseudo snub 24-cell consists of the union of three sets: 24-cell, another 24-cell and a new pseudo snub 24-cell.
We also derive a new representation for the symmetry group of the pseudo snub 24-cell and the corresponding vertices of the polytopes.
American Psychological Association (APA)
Koca, Nazifah O.& al-Qannubi, Amal J. H.& Koca, Muhammad. 2016. 4D pyritohedral symmetry. Sultan Qaboos University Journal for Science،Vol. 21, no. 2, pp.151-162.
https://search.emarefa.net/detail/BIM-720716
Modern Language Association (MLA)
al-Qannubi, Amal J. H.…[et al.]. 4D pyritohedral symmetry. Sultan Qaboos University Journal for Science Vol. 21, no. 2 (2016), pp.151-162.
https://search.emarefa.net/detail/BIM-720716
American Medical Association (AMA)
Koca, Nazifah O.& al-Qannubi, Amal J. H.& Koca, Muhammad. 4D pyritohedral symmetry. Sultan Qaboos University Journal for Science. 2016. Vol. 21, no. 2, pp.151-162.
https://search.emarefa.net/detail/BIM-720716
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references : p. 161-162
Record ID
BIM-720716