Cubic and ultimate groups of complete symmetry

Zheludev, IS (1964) Cubic and ultimate groups of complete symmetry. In: Proceedings of the Indian Academy of Sciences - Section A, 59 (4). pp. 191-202.

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Abstract

It is shown that the systems of definite actions described by polar and axial tensors of the second rank and their combinations during the superposition of their elements of complete symmetry with the elements of complete symmetry of the "grey" cube, result in 11 cubic crystallographical groups of complete symmetry. There are 35 ultimate groups (i.e., the groups having the axes of symmetry of infinite order) in complete symmetry of finite figures. 14 out of these groups are ultimate groups of symmetry of polar and axial tensors of the second rank and 24 are new groups. All these 24 ultimate groups are conventional groups since they cannot be presented by certain finite figures possessing the axes of symmetry {Mathematical expression}. Geometrical interpretation for some of the groups of complete symmetry is given. The connection between complete symmetry and physical properties of the crystals (electrical, magnetic and optical) is shown.

Item Type:	Journal Article
Publication:	Proceedings of the Indian Academy of Sciences - Section A
Publisher:	Indian Academy of Sciences
Additional Information:	Copyright of this article belongs to Indian Academy of Sciences.
Department/Centre:	Division of Physical & Mathematical Sciences > Physics
Date Deposited:	03 Jun 2010 06:37
Last Modified:	08 Jan 2013 06:01
URI:	http://eprints.iisc.ac.in/id/eprint/28077

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