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There are 15 types of convex pentagons are known to tile the plane monohedrally.

https://en.wikipedia.org/wiki/Pentagonal_tiling

I am wondering if all these 15 types pentagons are ruler and compass construction. If not, which of them can be (or not be) ruler and compass construction.

I have tried type 14 and 15 pentagons, both are ok.

John
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1 Answers1

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A small observation, a simple class of tiling pentagons are the ones that have two parallel sides. Clearly not all such pentagons can be constructed with ruler and compass. But then we can construct a whole lot of them, just draw two parallel lines, and then have some random choices.

orangeskid
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  • Yes, I would say type 1 can be constructed too. How about other types? – John Apr 20 '20 at 05:36
  • @John: I think you can build pentagons of each type, not all of them in a type but certainly a lot of generic ones. – orangeskid Apr 20 '20 at 06:01
  • Thanks, I do have a try, but some types cannot be constructed by me, such as type 9 and 11. I am looking for answer systematically. – John Apr 20 '20 at 06:13