Only three regular polygons can tessellate in a plane.

define tessellation
name the three regular polygons
explain why a regular polygon cannot form a tessellation.
explain why only these three can form a tessellation.

1. Define tessellation.

Tessellation is an arrangement of polygons in a repeated pattern without gaps or overlapping.

2. Name the three regular polygons.

Equilateral triangles, squares and regular hexagons are the only regular polygons that will tessellate.

3. Explain why a regular polygon cannot form a tessellation.

The interior angle of a polygon should divide 360 degrees evenly, so as to tessellate. The polygons whose internal angles do not divide 360 degrees do not tessellate. Like octagon is 135° which does not divide into 360°.

4. Explain why only these three can form a tessellation.

The triangles have an interior angle of 60 degrees that can divide 360 degrees. The square has interior angle of 90 degrees that divides 360 degrees.

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