Mirror Symmetries of the Cube

number of planes

1

cube opacity

0.7

Use the slider to show the nine planes of symmetry (or mirror planes) for the cube. If the center of the cube is the origin

(0,0,0)

and the

x

,

y

, and

z

axes are normal to opposite pairs of faces, the planes have equations

x=0

,

y=0

,

z=0

,

x=±y

,

y=±z

, and

z=±x

. With all nine cuts, each of the six faces of the cube is cut into eight triangles. For each such triangle, join its three vertices to the center of the cube to form a tetrahedron. These 48 tetrahedra partition the cube. (Reduce the opacity to see their interiors.)

External Links

Cubic Symmetry Types

Rotational Symmetries of Platonic Solids

Permanent Citation

Aaron Wallace

"Mirror Symmetries of the Cube"
http://demonstrations.wolfram.com/MirrorSymmetriesOfTheCube/
Wolfram Demonstrations Project
Published: November 23, 2015