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(111)
rotational planes and [111] axes of 3-fold symmetry |
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Finally, the cube has four (111) rotational planes and four [111] axes of 3-fold rota- |
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tional
symmetry. Unlike the (100) and (110) rotational planes modeled previously |
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these (111)
planes are not mirror planes. The [111] axes (not shown here) pass |
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Fig. 4a -
(111) cubic planes |
Fig. 4b
- (111) cubic planes, [110] axes |
(yellow, red, green,
orange) |
(yellow, red, green,
blue) |
Required
parts |
4 large triangles,
12 right triangles |
24 large triangles,
6 large squares |
18 pinges |
24 right triangles,
60 pinges |
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Fig. 4 -
Models of (111) cubic rotational planes and [110] 2-fold axes |
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through the corners
of the cube. Fig. 4a and b are views looking down one of the |
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four [111] 3-
fold axes which is perpendicular to one of the (111) planes. The lines |
of intersection
of the four (111) planes of Fig. 4b correspond to the cube's [110] axes |
of 2-fold
symmetry. |
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Exercise : Explain why the cube's (111) planes are not
mirror planes. |
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Geometry rules! - Cubic symmetry |