In the Euclidean plane, only three types of regular polygons can tessellate: equilateral triangles, squares, and regular hexagons. This is because their interior angles can perfectly add up to 360 degrees at each vertex. Other regular polygons, such as pentagons or octagons, do not meet this criterion and thus cannot tessellate the plane.
Triangle, square and hexagon
Equilateral triangle, square and regular hexagon.
If it's interior angle is a factor of 360 then it will tessellate such as a square, a regular hexagon and an equilateral triangle.
No. Equilateral heptagons (7 sided figures) do not tessellate the plane. Not if no other polygons are allowed. But if you allow a (non-equilateral) pentagon then you might be able to tessellate the plane!
The three regular polygons that can tessellate in a plane are equilateral triangles, squares, and regular hexagons. These shapes can fill a space without any gaps or overlaps because their interior angles are divisors of 360 degrees. Equilateral triangles have angles of 60 degrees, squares have angles of 90 degrees, and regular hexagons have angles of 120 degrees, all of which allow for complete tiling of the plane.
It has two regular polygons which can be used together to tessellate a plane.
Triangle, square and hexagon
Equilateral triangle, square and regular hexagon.
The answer depends on the size of the plane and of each polygon.
Equilateral triangle, square and regular hexagon.
Most regular polygons will not - by themselves. In fact, of the regular polygons, only a triangle, square and hexagon will. No other regular polygon will create a regular tessellation.
If it's interior angle is a factor of 360 then it will tessellate such as a square, a regular hexagon and an equilateral triangle.
No. Equilateral heptagons (7 sided figures) do not tessellate the plane. Not if no other polygons are allowed. But if you allow a (non-equilateral) pentagon then you might be able to tessellate the plane!
The three regular polygons that can tessellate in a plane are equilateral triangles, squares, and regular hexagons. These shapes can fill a space without any gaps or overlaps because their interior angles are divisors of 360 degrees. Equilateral triangles have angles of 60 degrees, squares have angles of 90 degrees, and regular hexagons have angles of 120 degrees, all of which allow for complete tiling of the plane.
All sorts of figures. The only regular polygons that can tessellate by themselves are triangles, squares and hexagons. Irregular polygons such as rectangles, rhombuses, parallelograms and trapeziums will as well. Regular octagons combined with squares will. Other regular polygons can be combined with appropriate star-shapes to tesselate. There are also Penrose tilings which, although they cover the plane, are non-periodic in the sense that the pattern does not repeat itself if you move along. Finally there are many irregular shapes that will tessellate.
No
A regular tessellation can only be formed by regular polygons with 3, 4, or 6 sides. These polygons are the equilateral triangle, square, and regular hexagon. Other polygons, such as pentagons or heptagons, cannot tessellate the plane without leaving gaps or overlaps. Thus, the applicable options for regular polygons in a regular tessellation are 3, 4, and 6 sides.