(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-

.

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

.

Jam308309(111)x4stcubetrans134x120res72gif255.gif (8808 bytes)

jam1971983foldcubeaniwhtbkgrnd90x96gif128.gif (7794 bytes)

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.

.

page 2 of lesson

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

page 4 of lesson

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