Q: What regular polygon that has an order of rotational symmetry of 5?

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A line segment would have rotational symmetry.

As the name suggests, they are polygons that have one or more lines of symmetry or rotational symmetry of order two or more. A symmetric polygon is not the same as a regular polygon.

If it's a regular 8 sided octagon then it rotational symmetry to the order of 8

If it is a regular 5 sided pentagon then its order of rotational symmetry is 5

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

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All of them have rotational symmetry because all the sides and angles have to be the same in order for the polygon to be a regular polygon

A line segment would have rotational symmetry.

As the name suggests, they are polygons that have one or more lines of symmetry or rotational symmetry of order two or more. A symmetric polygon is not the same as a regular polygon.

A regular nonagon with 9 sides has a rotational symmetry of 9.

If it is a regular octagon then it has rotational symmetry to the order of 8

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.

A shape like an equilateral triangle would therefore have an order of rotational symmetry of 3

If it is a regular octagon then it has rotational symmetry to the order of 8

If it's a regular 8 sided octagon then it rotational symmetry to the order of 8

It has both because it has 5 lines of symmetry and rotational symmetry to the order of 5

Any regular polygon of n sides, has an order of symmetry of n. Therefore, since a nonagon has nine sides, a nonagon has an order of symmetry of 9.

heck yeah it does * * * * * It can do, but it need not have any non-trivial rotational symmetry. A regular decagon will have rotational symmetry of order 10.