Triangle, square and hexagon
Equilateral triangle, square and regular hexagon.
No.
yes no yes no
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.
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.
Equilateral triangle, square and regular hexagon.
Equilateral triangle, square and regular hexagon.
No.
No.
yes no yes no
It has two regular polygons which can be used together to tessellate a plane.
The answer depends on the size of the plane and of each polygon.
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.
No not normally
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.
yes
No, a regular isosceles triangle will not tessellate. In order for a shape to tessellate, it must be able to fit together with copies of itself without any gaps or overlaps. Regular isosceles triangles have angles of 90, 45, and 45 degrees, which do not allow for a repeating pattern that covers a plane without any spaces. Regular polygons that tessellate include equilateral triangles, squares, and hexagons.