Equilateral triangle, square and regular hexagon.
Triangle, square and hexagon
Equilateral triangle, square and regular hexagon.
No.
No.
No not normally
yes
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.
The answer depends on the size of the plane and of each polygon.
The rectangle is the simplest and most obvious case of a geometrical form that can tile a plane.
It has two regular polygons which can be used together to tessellate a plane.