Polymorf - Knowhere - Cubic symmetry

(111) rotational planes and [111] axes of 3-fold symmetry

Finally, the cube has four (111) rotational planes and four [111] axes of 3-fold rota-

tional symmetry. Unlike the (100) and (110) rotational planes modeled previously

these (111) planes are not mirror planes. The [111] axes (not shown here) pass


Fig. 4a - (111) cubic planes	Fig. 4b - (111) cubic planes, [110] axes
(yellow, red, green, orange)	(yellow, red, green, blue)
Required parts
4 large triangles, 12 right triangles	24 large triangles, 6 large squares
18 pinges	24 right triangles, 60 pinges
.

Fig. 4 - Models of (111) cubic rotational planes and [110] 2-fold axes

through the corners of the cube. Fig. 4a and b are views looking down one of the

four [111] 3- fold axes which is perpendicular to one of the (111) planes. The lines

of intersection of the four (111) planes of Fig. 4b correspond to the cube's [110] axes

of 2-fold symmetry.

Exercise : Explain why the cube's (111) planes are not mirror planes.

Page 3 Geometry rules! - Cubic symmetry