Q: What is the order of rotational symmetry of a parallelogram?

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A general parallelogram has rotational symmetry of order two.

no shape does! * * * * * Not true. A parallelogram has rotational symmetry of order 2, but no lines of symmetry.

Parallelogram.

A parallelogram has no lines of symmetry, but it has rotational 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.

Related questions

parallelogram * * * * * A parallelogram does have rotational symmetry (order 2).

A general parallelogram has rotational symmetry of order two.

A parallelogram has rotational symmetry of order 2.

no shape does! * * * * * Not true. A parallelogram has rotational symmetry of order 2, but no lines of symmetry.

2

To the order of 2

A parallelogram has a rotational symmetry of 2!

parallelogram

Parallelogram.

A parallelogram has rotational symmetry of order 2 but there are no lines of symmetry.

Yes, rotational symmetry of order 2.

Nope - it has rotational symmetry.