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What is Rotational Symmetry?

A Rotation is a transformation of a shape around a central point.

You are watching: Does a pentagon have rotational symmetry


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In each diagram in the series above, the shape is rotated an equal amount. In each position the overall shape is the same as the original position.

What is the Order of Rotational Symmetry?

The order of rotational symmetry is the number of times the shape is the same as the original through 360 degrees. In all the diagrams we have looked at so far the order of rotation has been 5. The diagrams have all shown that the original can be turned 4 times to match the original. Making a total of 5 positions within 360 degrees which are all the same.

The diagrams so far have all been of a form of the pentagonal archetype. An archetype is a shape that expresses the symmetry of that number.

‘What is Rotational Symmetry?’ Factsheet and Rotational Symmetry Hunt sheet – are Free downloads available in the resource library

What is the order of rotational symmetry of a regular pentagon?


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This 5 point star displays the same order of rotational symmetry as our other shapes so far. The 5 point star features in nature and when we see it we be able to see the rotational symmetry of the pentagon present in natural form.


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How many orders of rotational symmetry does a pentagon have?

This all depends on whether it is a regular pentagon or not.

How does Rotational Symmetry work in nature?

So much of the symmetry we see in nature we take for granted we almost don’t even realise we are seeing it, that’s how used to it we are. But it is there and we can learn to see it anew.

What is important to remember here is that we are observing nature’s patterns and our understanding of these patterns is from a very maths centric point of view. Nature doesn’t actually rotate to produce these – at least not in the sense we are talking about here. What we see in nature is a manifestation of the phase appearance of a rotation.

In nature we see rotational symmetry mostly in the plant kingdom. We also see it in the animal kingdom in marine life.

Rotational symmetry in nature presents to us in two forms: Asymmetrical rotation and combined rotational and bilateral symmetries

Rotational Symmetry in marine life

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examining the rotational order of 5 within the face of flowers

By examining the face of flowers with the rotational order of 5 we can come to understand the symmetry present within the 5 archetype. There is an experience of the infinite nature of the five archetype that we can relate to when we work with nature in this way. And understand our relationship to it. Spend calm moments examining and threading the patterns onto the flower in these Stitch Upon a Star kits.

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Every flower form that has equally spaced petals or sepals around a centre displays rotational symmetry. This diagram has rotational symmetry of order five, it just isn’t combined with bilateral symmetry. Each shape that is rotated around the centre is asymmetrical in itself. This doesn’t alter the rotational symmetry and its order.

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This cyclamen flower displays approx rotational symmetry around its centre. Unlike the primrose or vinca it doesn’t have bilateral symmetry in its petals and therefore the face of the flower doesn’t display the combined symmetries

Other petalled flowers give us opportunity to embrace other orders of rotational symmetries. We can examine nature and read the varying orders of rotational symmetry. Often all we need to do is count the petals.