
(111)
rotational planes and [111] axes of 3fold symmetry 
. 

Finally, the cube has four (111) rotational planes and four [111] axes of 3fold rota 
. 

tional
symmetry. Unlike the (100) and (110) rotational planes modeled previously 
. 

these (111)
planes are not mirror planes. The [111] axes (not shown here) pass 
. 



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 
. 


. 

Fig. 4 
Models of (111) cubic rotational planes and [110] 2fold axes 
. 


. 

through the corners
of the cube. Fig. 4a and b are views looking down one of the 
. 
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 2fold
symmetry. 
. 

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


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Geometry rules!  Cubic symmetry 