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Although objects themselves may appear to have 5-fold, 7-fold, 8-fold, or higher-fold rotation axes, these are not possible in crystals. Crystals can only show 2-fold, 3-fold, 4-fold, or 6-fold rotation axes. The reason is that the external shape of a crystal is based on a geometric arrangement of atoms. In fact, if we try to combine objects with 5-fold and 8-fold apparent symmetry, we cannot combine them in such a way that they completely fill space, as illustrated below: 61 ÷ 7.55
Submitted by Diane P. Sep. 24, 2021 04:55 a.m.
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