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You will always end up with empty space.
Can you tile a floor with regular pentagons. Floor tiles are used on floors. No not if your floor is flat. In 2015 the 15th type was. You might need to rotate it to make sides of the same length line up but you can always tile the plane with it.
Wall tiles are used on walls. If you want to interchange. You will always end up with empty space. But by easing angle and length constraints you can find types of convex pentagons that fit together neatly to cover a surface.
In contrast regular hexagons do cover the plane as seen in the floor tiles used in washington s metrorail stations. It looks like your tiles can also tile the plane periodically that s what happens in each of the five sectors of the plane that meet at the central pentagon. So far we know of 15 types of pentagons which could fill the tile many described by reinhardt himself several identified by other mathematicians even amateurs. You can make the.
Regular pentagons do not tile the plane. Regular pentagons do not tile the plane. Or take any triangle.
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