Tessellating Octagons?

Geometry Level 3

Does there exist an octagon (not necessarily convex) which can tessellate the plane?

Yes No

Calvin Lin by Calvin Lin

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3 solutions

Marta Reece
Jan 11, 2018

Just one possibility out of many

5 Helpful 0 Interesting 1 Brilliant 0 Confused

Moderator note:

Note: There is no convex polygon with 7 or more sides that tessellates the plane. However, this requires quite a bit more theory to prove.

David Vreken
Jan 12, 2018

There are several possibilities. One method to find a tessellating octagon is to take an existing tessellating shape with less sides, such as a square, and break it up into congruent octagons, like this:

or this:

3 Helpful 0 Interesting 0 Brilliant 0 Confused

an other one:

1 Helpful 0 Interesting 0 Brilliant 0 Confused

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