(111) rotational planes and  axes of 3-fold symmetry

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Finally, the cube has four (111) rotational planes and four  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  axes (not shown here) pass

.  Fig. 4a -  (111) cubic planes Fig. 4b -  (111) cubic planes,  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  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  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  axes

of 2-fold symmetry.

. Exercise : Explain why the cube's (111) planes are not mirror planes. Back to Knowhere