Cubic symmetry .
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The cube has nine mirror planes, thirteen axes of rotational symmetry, and seven-

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teen planes of rotational symmetry.

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(100) mirror planes and  axes of 4-fold rotational symmetry

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The cube has three (100) mirror planes parallel to its three sets of opposed faces.

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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
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correspond to the cube's three (100) planes of 4-fold rotational symmetry.

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The lines of intersection of these planes correspond to the cube's three  axes of 4-fold symmetry.  Each axis is perpendicular to
the center point of its corresponding rotational plane.  Rotating the
cube around these axes reveals the 4-fold symmetry. (Note: the
axes can be highlighted by coloring the pinges aligned with them

the same color as their corresponding planes.)

Fig 2  4-fold 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  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.