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Which regular polygon can be used to form a tessellation

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Final answer:

Only three regular polygons can tessellate, which are triangles, squares, and hexagons, as their internal angles evenly divide into 360 degrees allowing them to fit together without gaps.

Step-by-step explanation:

A tessellation is a pattern of shapes that fit perfectly together without any gaps or overlaps. When it comes to regular polygons, there are exactly three that can tessellate: triangles, squares, and hexagons. Each of these shapes has internal angles that are divisors of 360 degrees, which allows them to fit together evenly on a flat surface. Although hexagons can indeed tessellate, for some lattice structures, a rhombus may be preferred for its simplicity, despite not being a regular polygon.

The condition for a tessellation is that the interior angles of the polygon must add up to a multiple of 360 degrees when they meet at a point. For example, the interior angle of a regular triangle is 60 degrees, and six triangles can meet at a point (6 x 60 = 360). Similarly, a square has an interior angle of 90 degrees and four can meet at a point (4 x 90 = 360), and a regular hexagon has an interior angle of 120 degrees with three meeting at a point (3 x 120 = 360).

User Kwicher
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Final answer:

A hexagon can be used to form a tessellation.

Step-by-step explanation:

A regular polygon that can be used to form a tessellation is a hexagon. A tessellation is when a shape is repeated to completely cover a plane without any gaps or overlaps. The sides of a regular hexagon fit perfectly together to create a tessellation.

For example, you can create a tessellation of hexagons by aligning them so that each side of one hexagon is adjacent to a side of another hexagon.

Other regular polygons, such as squares, do not tessellate by themselves because the angles and sides do not fit perfectly together.

User Freewalker
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