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# Polygon Rings

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Age 11 to 14

Challenge Level

Here is a pattern made of regular pentagons:

If the pattern continued, do you think it will form a complete loop or will the pentagons overlap?

Try it using the Tessellation Interactivity below.

*If you've never used the interactivity before, there are some instructions and a video.*

Once you've had a chance to explore, here are some questions you might like to consider.

How many pentagons form a ring?

How many decagons would form a ring?

Why do they fit together so neatly without overlapping or leaving a gap?

What about other polygons?

Can you always make a ring?

Is there a way to predict how many polygons you need to form a ring?

*With thanks to Don Steward, whose idea inspired this problem.*