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).