###### Asked in Geometry

Geometry

# What does order of rotational symmetry mean?

## Answer

###### Wiki User

###### April 13, 2012 11:15AM

The order of symmetry of an object is the number of part-rotations that bring the object to a position that is identical to its starting position. Note that since all objects must return to their starting position if rotated through one whole circle (360 degrees), rotational symmetry of 1 is not counted.

## Related Questions

###### Asked in Math and Arithmetic, Algebra, Geometry

### How do you sketch a figure with rotational symmetry but no line symmetry?

When a shape is rotated about its centre, if it comes to rest in
a position and looks exactly like the original, then it has
rotational symmetry.
A shape like an equilateral triangle would therefore have an
order of rotational symmetry of 3. The general rule for a regular
polygon (shapes such as pentagons, heptagons, octagons etc. is,
that the number of sides is the same as the number of lines of
symmetry, which is also the same as the
rotational symmetry order). This means that a regular hexagon
has 6 sides, 6 lines of symmetry and an order of rotational
symmetry of 6.
Following from this, then a square, which is a regular polygon,
has 4 sides, 4 lines of symmetry and an order of rotational
symmetry of 4.
If a shape has rotational symmetry, it must have either line
symmetry or point symmetry or both. For example, a five pointed
star has 5 lines of symmetry and rotational symmetry of order 5,
but does not have point symmetry. A parallelogram has no line of
symmetry, but has rotational symmetry of order 2 and also point
symmetry.
Only a shape which has line symmetry or point symmetry can have
rotational symmetry. When there is point symmetry and also
rotational symmetry, the order of the latter is even. For example,
the letter 'S' has rotational symmetry of order 2, the regular
hexagon of order 6.
On this basis, we would suggest that the letter 'F' does not
have a rotational symmetry order as it does not have either line
symmetry or point symmetry. It doesn't have a centre around which
you could rotate it. Sounds weird, but given the definitions, we
think this is the case.