ورقة بحثية
4D Pyritohedral Symmetry = تماثل متعدد الأوجه ذو التركيب المشابه لمعدن البايريت في الفضاء الأقليدي ذو الأبعاد الأربعة

Koca, Nazife Ozdes.


 

4D Pyritohedral Symmetry = تماثل متعدد الأوجه ذو التركيب المشابه لمعدن البايريت في الفضاء الأقليدي ذو الأبعاد الأربعة

Koca, Nazife Ozdes.

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.

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 th...

مادة فرعية

المؤلف : Koca, Nazife Ozdes.

مؤلف مشارك : Al Qanobi, Amal J.H
Koca, Mehmet

بيانات النشر : Muscat، Sultanate of Oman : Sultan Qaboos Journal of Science، 2016مـ.

التصنيف الموضوعي : العلوم البحتة| .

المواضيع : Physics .

الفيزياء .

رقم الطبعة : 2

المصدر : Sultan Qaboos University : Muscat، Sultanate of Oman.

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