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Well, pentagons that tile a plane need to have angles and side lengths that have one or more in the shape.

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Q: Why do some pentagons tile the plane and others don't?
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Related questions

Are pentagons congruent?

Some are some are not. Two regular pentagons with one equal side are congruent.


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Can a regular pentagon be used to tile a floor?

No, not if your floor is flat. Regular pentagons do not tile the plane. You will always end up with empty space. You would need to use some other shapes too (or irregular pentagons) http://www2.spsu.edu/math/tile/defs/pentagon.htm


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