(110) mirror planes, (110) rotational planes, and  axes of 2-fold 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  axes .
2-fold rotational symmetry.   The cube's six  axes of 2-fold 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  axes).  Fig. 3a

gives view of the cube looking down a  rotational axis to show the 2-fold 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.

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Exercise:   What properties do the (100) and (110) cubic planes and the  and  cubic axes have in common?  How do they differ?

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