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All triangles will tessellate. All quadrilaterals will tessellate

There are 15 classes of convex pentagons - the latest discovered in 2015 - which will tessellate.

Regular hexagons will tessellate. In addition, there are 3 classes of irregular convex hexagons which will tessellate.

All other convex polygons will not tessellate.

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Q: What shapes don't tessellation?
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