
Cubic symmetry 
. 
. 
The
cube has nine mirror planes, thirteen axes of rotational symmetry, and seven 
. 
teen
planes of rotational symmetry. 
. 
(100)
mirror planes and [100] axes of 4fold rotational symmetry 
. 
The cube has three (100) mirror planes parallel to its three sets of opposed faces. 
. 
Note
how each slices the cube into two identical halves. These mirror planes also 
. 

. 
. 
Fig. 1  (100) mirror planes of the cube 
(shown in red, purple, and orange) 
Required parts  32 squares, 50 pinges 

. 
correspond
to the cube's three (100) planes of 4fold rotational symmetry. 
. 
The lines of intersection of
these planes correspond to the cube's 

three [100] axes of 4fold
symmetry. Each axis is perpendicular to 
the center point of its
corresponding rotational plane. Rotating the 
cube around these axes reveals
the 4fold symmetry. (Note: the 
axes can be highlighted by
coloring the pinges aligned with them 
the same color
as their corresponding planes.) 
Fig 2 4fold axis 

Exercise: After you build this Polymorf model instruct
someone to stand behind you 

with it and make you guess whether they rotated the model
around a [100] axis or 
not. If you can't tell if they did or not when you
turn around to look at it again then 
you know that
the cube is symmetrical about that
axis. 



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1 Geometry rules!  Cubic symmetry 