Can we set up a mirror so that an object looks the same in front of the mirror
as in the mirror? The word MUM has mirror symmetry, but HAM does not; MUM
in front of the mirror is the same as MUM in the mirror while HAM becomes
MAH. A tripod has mirror symmetry, but the triskelion (tripod with feet) does
not. The triskelion as the object before the mirror is right-handed but its mirror
image in what is called the image plane is left-handed.
Rotational symmetry
We can also ask whether there is an axis perpendicular to the page so that the
object can be rotated in the page through an angle and be brought back to its
original position. Both the tripod and the triskelion have rotational symmetry.
The triskelion, meaning ‘three legs’, is an interesting shape. The right-handed
version is a figure which appears as the symbol of the Isle of Man and also on
the flag of Sicily.
If we rotate it through 120 degrees or 240 degrees the rotated figure will
coincide with itself; if you closed your eyes before rotating it you would see the
same triskelion when you opened them again after rotation.
The Isle of Man triskelion
The curious thing about the three-legged figure is that no amount of rotation
keeping in the plane will ever convert a right-handed triskelion into a left-handed
one. Objects for which the image in the mirror is distinct from the object in front
of the mirror are called chiral – they look similar but are not the same. The
molecular structure of some chemical compounds may exist in both right-handed
and left-handed forms in three dimensions and are examples of chiral objects.