Polymorf - Knowhere - Cubic symmetry

Cubic symmetry

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

teen planes of rotational symmetry.

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

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

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

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

The lines of intersection of these planes correspond to the cube's

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

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 [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.

Page 1 Geometry rules! - Cubic symmetry