Symmetry of the Pyritohedron and Lattices

Authors

Nazife O. Koca, Department of Physics, College of Science, Sultan Qaboos University, P.O. Box 36, PC 123 Al-Khoud, Muscat, Sultanate of Oman
Aida Y. Al-Mukhaini, Department of Physics, College of Science, Sultan Qaboos University, P.O. Box 36, PC 123 Al-Khoud, Muscat, Sultanate of Oman
Mehmet Koca, Department of Physics, College of Science, Sultan Qaboos University, P.O. Box 36, PC 123 Al-Khoud, Muscat, Sultanate of Oman
Amal J. Al-Qanobi, Department of Physics, College of Science, Sultan Qaboos University, P.O. Box 36, PC 123 Al-Khoud, Muscat, Sultanate of Oman

Abstract

The pyritohedron consisting of twelve identical but non regular pentagonal faces and its dual pseudoicosahedron that possess the pyritohedral (Th) symmetry play an essential role in understanding the crystallographic structures with the pyritohedral symmetry. The pyritohedral symmetry takes a simpler form in terms of quaternionic representation. We discuss the 3D crystals with the pyritohedral symmetry which can be derived from the Coxeter-Dynkin diagram of D3.

Recommended Citation

Koca, Nazife O.; Al-Mukhaini, Aida Y.; Koca, Mehmet; and Al-Qanobi, Amal J. (2016) Symmetry of the Pyritohedron and Lattices, Sultan Qaboos University Journal For Science: Vol. 21: Iss. 2, 139-149.
DOI: https://doi.org/10.24200/squjs.vol21iss2pp139-149
Available at: https://squjs.squ.edu.om/squjs/vol21/iss2/2