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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 [100] 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 |
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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 |
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three [100] 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 |
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Exercise: After you build this Polymorf model instruct
someone to stand behind you |
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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 |