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Q: Does a regular hexagon tesselate

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Triangle, square, hexagon.

yes definitely you can tesselate a regular haxagon

Yes; it will form a honey-comb shape. <http://gwydir.demon.co.uk/jo/tess/bighex.gif> for image.

No only three can tesselate. they are: An equilateral triangle, a square and a 6 sided hexagon.

By themselves, only 3: triangle, square and hexagon. But there are combinations: eg octagon + square.

Yes they do. In fact the honeycomb that bees make is a natural tessellation of the hexagon.

yes there are several ways to tesselate this figure.

You can do that by simply proving that the hexagon is a regular hexagon. You could do this by dividing the hexagon into 6 equilateral triangles of the same size successfully that tesselate to form a hexagon, thus proving that all sides are equal.

Yes. Tessellated hexagons are the basis of many natural structures such as honeycombs.

No.

No, you cannot.

No, it cannot.

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