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A simple arrangement and notation of the thirty-two classes of symmetry based on the symmetry of zone-axes

Published online by Cambridge University Press:  14 March 2018

John W. Evans
John W. Evans*
Affiliation:
Imperial Institute and Birkbock College
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Extract

If a straight line making an angle with a zone-axis of a crystal be rotated about the zone-axis while the crystal remain fixed, the physical characters of that line will pass through a cycle of changes. If these changes repeat themselves n times during the course of a complete revolution, the zone-axis is said to have an nth-turn or n-fold cyclic symmetry. If the line be at any time normal to a crystal-face it will be normal to a face with the same physical characters n times during such a revolution.

Type
Research Article
Information
Mineralogical magazine and journal of the Mineralogical Society , Volume 14 , Issue 67 , September 1907 , pp. 360 - 364
Copyright
Copyright © The Mineralogical Society of Great Britain and Ireland 1907

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References

Page 360 note 1 The number of the planes of symmetry passing through a bilateral zone-axis is that of its cyclic symmetry. If this number be odd, they are all like ; if it be even, they fall into two equal groups of unlike planes. A unilateral zoneaxis has no planes of symmetry passing through it.

Page 361 note 1 The number of secondary axes will be equal to that of the cyclic symmetry of the original axis. If that be odd, they will be all alike and uniterminal. If it be even, there will be two equal groups of unlike helical axes.

If a straight line at right angles to a helical zone-axis be rotated about it, the order of succession of changes of physical characters will be the same for opposite directions of rotation, except that the relation of such characters to opposite ends of the zone-axis will be reversed. In like manner and subject to a similar proviso, the faces of a helical zone exhibit the same succession in opposite directions. These relations do not exist in the case of other unilateral zone-axes.

Page 362 note 1 It is convenient to arrange the different kinds of longitudinal symmetry in an order different from that in which they have been described.

Page 364 note 1 Min. Mag., 1907, vol. xiv, p. 261.