It is known that the sum of the exterior angles of a convex polygon is always 360º. Since an exterior angle of a right angle is also a right angle, our four right angles would take up the entire 360º ...

Why Can’t Convex Polygons With More Than Six Sides Tile the Plane? Consider seven-sided heptagons, and, for simplicity, consider only vertex-to-vertex tilings (having vertices in the middle of edges ...

No convex polygon with more than 6 sides can tile the plane (because of simple angle arguments). Pentagons were the final holdout. Editorial Standards Reprints & Permissions.

To refresh your geometry, convex polygons are closed figures that don’t have any internal angles that are more than 180 degrees. ... see the image of a convex polygon on the left.