For example, consider this butterfly.
The butterfly has reflective symmetry, because we can draw the dotted line through a part of the butterfly and the resulting pieces are mirror images of each other.
The total order of symmetry of an object is the sum of the object’s order of rotational symmetry and its number of lines of reflection.
Mandalas exhibit a lot of rotational and reflective symmetry.
Consider the mandala below in applying the concepts that we have just discussed: angle of symmetry, order of rotation, lines of symmetry, and total order of symmetry.
This mandala’s angle of symmetry is 45°. This is the smallest angle by which we can rotate it to produce an identical configuration.
Its order of rotation is 360° ÷ 45° = 8. The number of angles less than or equal to 360° by which we can rotate the mandala to get the same image is eight.
We can also see that this mandala has eight lines of reflection. Each of these eight lines divide the mandala into mirror image halves.
Therefore, the mandala’s total order of symmetry is equal to 8 + 8 = 16.