Rotational Symmetries of Platonic Solids

angle

solid

tetrahedron

cube

octahedron

dodecahedron

icosahedron

axis

center to vertex

mid-edge to mid-edge

center to face

Set

:Lists {a$2573,b$2573,c$2573,d$2573,e$2573,f$2573} and {4,5,6} are not the same shape.

A symmetry of a figure moves a copy of the figure to coincide with its original position. Beside the rotations shown here, the other symmetries of the Platonic solids are reflections in various planes through the center. Symmetries are motions and form a group. If

p

and

q

are symmetries,

p∘q

is also a symmetry: move the figure with

q

, then move the new position with

p

. Try to understand how the rotations shown in this Demonstration combine.