The more ways a shape can be reflected and turned to fit onto itself, the more symmetry it has.
Plane shape have two kinds of symmetry :
- When a shape can be reflected onto itself about a line it
has line symmetry
- When a shape can be rotated about a point through an angle
of less than 360o to coincide with itself it has rotational symmetry.
A Toblerone box, for example, has 4 planes of symmetry: 3 like
the one shown along the length of the box, and 1 halfway along at
right angles to the box, containing the red triangle. It also has
4 axes of rotational symmetry. One of these is the line through
the mid-point of both its ends, about which it has rotational symmetry
of order 3. The other three are like the one drawn with a red dashed
line. The box fits onto itself after a half-turn about each of these
axes, so has rotational symmetry of order 2 about them.