Abstract
IN Barlow's paper1 on the “Probable Nature of the Internal Symmetry of Crystals” he writes: “A fifth kind of symmetry … bears the same relation to the fourth kind as the second bears to the third; that is to say, it may be regarded as produced by the insertion of additional points in positions midway between points arranged in the fourth kind of symmetry”. This is not so. Barlow did not describe or figure that arrangement which does bear the same relation to the fourth kind which the second bears to the third. It is shown in the accompanying figure. Its triangular base and first two layers are the same as those of Barlow's “second kind of symmetry”; but its third layer lies over the first, the fourth over the second, and so on. If now we insert additional points in positions midway between points in this structure, Barlow's “fifth kind of symmetry” is produced.
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References
Barlow, W., NATURE, 29, 186 (1883).
Tait, P. G., Proc. Roy. Soc. Edin., 4, 535 (1862), arrangements iii and iv.
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MELMORE, S. Symmetrical Arrangement of Equal Spheres. Nature 146, 199 (1940). https://doi.org/10.1038/146199a0
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DOI: https://doi.org/10.1038/146199a0
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