Get Practice 1 Identifying Tessellations

Equilateral triangles, squares and regular hexagons are the only regular polygons that will tessellate. Therefore, there are only three regular tessellations. 3.

A pattern of shapes that fit perfectly together! A Tessellation (or Tiling) is when we cover a surface with a pattern of flat shapes so that there are no overlaps or gaps.

A shape is said to tessellate the plane if the plane can be covered without holes and no overlapping (save for the boundary points) with congruent copies of the shape. Squares, rectangles, parallelograms, trapezoids tessellate the plane; each in many ways.

Yes, a scalene triangle does tessellate. The reason we can create a tessellation with a scalene triangle is because we can connect any two congruent...

There are only three shapes that can form such regular tessellations: the equilateral triangle, square, and regular hexagon. Any one of these three shapes can be duplicated infinitely to fill a plane with no gaps. Many other types of tessellation are possible under different constraints.

A Tessellation (or Tiling) is when we cover a surface with a pattern of flat shapes so that there are no overlaps or gaps. A regular tessellation is a pattern made by repeating a regular polygon. A semi-regular tessellation is made of two or more regular polygons. The pattern at each vertex must be the same!

To tessellate means that congruent figures are put together to create a pattern where there aren't any gaps or spaces in the pattern. Figures can be put side by side and/or upside down to create the pattern. The pattern is called a tessellation. If you look at the honeycomb, you can see that hexagons are tessellating.

A square has an interior angle of 90°, so 4 squares fit together to make 360°: 360 ÷ 90 = 4. An equilateral triangle has an interior angle of 60°, so 6 triangles fit together to make 360°: 360 ÷ 60 = 6. A hexagon has an interior angle of 120°, so 3 hexagons fit together to make 360°: 360 ÷ 120 = 3.

2. Which regular polygons will tessellate on their own without any spaces or overlaps? Equilateral triangles, squares and regular hexagons are the only regular polygons that will tessellate. Therefore, there are only three regular tessellations.

Every shape of quadrilateral can be used to tessellate the plane. In both cases, the angle sum of the shape plays a key role. Since triangles have angle sum 180° and quadrilaterals have angle sum 360°, copies of one tile can fill out the 360° surrounding a vertex of the tessellation.