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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.
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