(110) mirror planes, (110) rotational planes, and [110] 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

cube.gif (7654 bytes)

cube.gif (11672 bytes)

cube.gif (9754 bytes)

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

2-fold rotational symmetry.   The cube's six [110] 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 [110] axes).  Fig. 3a

gives view of the cube looking down a [110] 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. 


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

page 1 of lesson

page 3 of lesson

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

Back to Knowhere

Home page

Page 2    Geometry rules! - Cubic symmetry


home   sitemap   products   Polywood   .networks   contact us   Knowhere   3Doodlings