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What shapes have rotational symmetry?

Updated: 4/28/2022
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squares

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Q: What shapes have rotational symmetry?
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Continue Learning about Geometry

What is the rotational symmetry of a trapezoid?

A trapezium does not have rotational symmetry.


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.


Does z have rotational symmetry but no line symmetry?

The letters H and Z have both line symmetry and rotational symmetry


How much rotational symmetry does an octagon have?

It has 8lines of rotational symmetry


Does an equilateral triangle have rotational symmetry?

yes it does. It a rotational symmetry of 3

Related questions

What kind of shapes don't ever have rotational symmetry?

Irregular shapes don't ever have rotational symmetry.


What shape has a rotational symmetry of order 1?

none shapes have 1 rotational symmetry because in rotational symmetry one is none


What shapes have 1 order of rotational symmetry?

Nothing has 1 order of rotational symmetry because in rotational symmetry 1 is none.


What shapes has rotational symmetry?

A star


Which shapes have no rotational symmetry?

circle


Which shapes have rotational symmetry which is a quadrilateral?

squarerhombusdiamondrectangle


What figure has rotational symmetry but not line symmetry?

A nonrectangular parallelogram has rotational symmetry, but not line symmetry. Additionally, shapes such as the letters S, N, and Z can be rotated to show rotational symmetry, although they do not have line symmetry.


How many rotational symmetry does a cuboid has?

None normally because rotational symmetry is only applicable to 2 dimensional shapes such as polygons.


What are 3 shapes that have rotation symmetry?

A circle, square, and a triangle all have rotational symmetry.


What rotation symmetry does a regular hexagon have?

A regular hexagon has rotational symmetry of 6. Usually we can figure out the rotational symmetry of most shapes by looking at how many sides they have. Such as an octagon has rotational symmetry of 8 ect. Hope it helped!


Which shape has 1 order of rotational symmetry?

These are also known as asymmetric shapes.


What is the symmetry of sphere?

Three dimensional shapes, generally, don't have lines of symmetry, but a circle has an infinite number is symmetry lines. 3D shapes also don't have rotational symmetry either, but a circle has an infinite number of that as well.