Shapes that tessellate

Index --- grids --- squares (examples) --- triangles (examples) --- Escher-style (examples) --- for teachers

Triangles, squares and hexagons are the only regular shapes which tessellate by themselves. You can have other tessellations of regular shapes if you use more than one type of shape. You can even tessellate pentagons, but they won't be regular ones. Tessellations can be used for tile patterns or in patchwork quilts!

Single regular shapes	Triangles Squares Hexagons	Large grid of triangles Large grid of squares Large grid of hexagons

Multiple regular shapes	Squares, triangles Hexagons, triangles Hexagons, squares, triangles Octagons, squares Dodecagons, triangles Dodecagons, hexagons, squares	Large grid of squares and triangles Large grid of hexagons and triangles Large grid of hexagons, squares and triangles Large grid of octagons and squares Large grid of dodecagons and triangles Large grid of dodecagons, hexagons and squares

Other shapes	Irregular pentagons Waffle pattern Fish patterns	Large grid of irregular pentagons Large grid of waffle pattern Large grid of fish patterns

Triangles - these make pretty tessellations. Two triangles make a diamond. Six triangles make a hexagon.

Design a triangle tessellation online
More examples of triangle tessellations
Large grid of triangles to print or save

Design a triangle mosaic online - which you can use to make tessellations

Squares - rather obvious! By colouring them, you can build up more complicated patterns. Click here to make a square tessellation online. Make an Escher-style tessellation online

Design a square tessellation online
Design an Escher-style tessellation online
Optical illusions based on tessellations
Large grid of triangles to print or save

Design mosaics online - which you can use to make tessellations

Hexagons - Bees make natural tessellations of hexagons in their honeycombs.

Hexagons can be made with triangle grids.
Design a triangle tessellation online
Design a triangle mosaic online

Large grid of hexagons to print or save

Squares and triangles - There are two ways to mix squares and triangles in the same pattern.

This is the boring way. You can make it more interesting with colouring.

The other grid looks strange, as we don't recognise squares as easily when they are tilted.

Large grids of triangles and squares to print or save - both types

Hexagons and triangles - There are two regular ways to mix hexagons and triangles in the same pattern. You can play around with the triangles grid to find other ways to mix hexagons and triangles.

This packs the triangles closely, with a few triangles between.

Here, the hexagons are further apart, with a line of triangles between them.

These tessellations can be made with triangle grids.
Design a triangle tessellation online
Design a triangle mosaic online

Large grids of triangles and hexagons to print or save - both types

Hexagons, squares and triangles

Large grid of hexagons, squares and triangles to print or save

Octagons (8 sides) and squares

Large grid of octagons and squares to print or save

Dodecagons (12 sides) and triangles - Since the sides of the shapes must be the same length, so they can fit together, you end up with the dodecagons being much larger than the triangles.