
(110) mirror
planes, (110) rotational planes, and [110] axes of 2fold rotational symmetry 


The cube also has six (110) planes of mirror symmetry passing through its six sets of 


opposite edges. The
planes slice diagonally through each face, dividing the cube into 


identical halves. These
mirror planes also correspond to the cube's six (110) planes of 





Fig. 3a  One (110)
plane 
Fig. 3b  Two (110)
planes 
Fig. 3c  Six (110)
planes 

Required parts 

4 small squares 
16 small squares 
24 small squares 
4 right triangles 
16 right triangles 
12 right triangles 
1 rectangle, 14
pinges 
8 rectangles, 58
pinges 
6 rectangles, 66
pinges 
. 


Fig. 3 Alternative models for
demonstrating (110) cubic planes and [110] axes 
. 





2fold rotational symmetry.
The cube's six [110] axes of 2fold rotational symmetry that 


correspond to these six
rotational planes are perpendicular to the center points of each 


respective plane on a line
passing through the midpoints of its opposite edges (use axles 

colored the
same as their respective planes to highlight these [110] axes). Fig. 3a 

gives view of the cube looking
down a [110] rotational axis to show the 2fold symmetry. 

Fig.
3b shows only two of the (110) planes intersecting due to the complexity of modeling 


all
six planes simultaneously. Instead, in Fig. 3c each plane is projected outside of
the 


centermost
cube. Viewing the model face on projects the (110) diagonal planes back 


into
the center of the cube in kaleidoscopic fashion. 

. 

Exercise: What
properties do the (100) and (110) cubic planes and the 


[100] and [110] cubic axes have in
common? How do they differ? 

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Geometry rules!  Cubic symmetry 