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.