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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.

Large grid of dodecagons and triangles to print or save




Dodecagons, hexagons and squares

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




Pentagons - Regular pentagons won't make a tessellation, but rather squashed ones will.

Large grid of irregular pentagons to print or save

Penrose tiles - these are based on five-fold symmetry, and they never repeat! (external site.)




Waffle - You don't have to restrict yourself to regular shapes. Here is a waffle pattern, and a suggested colour scheme.

Large waffle grid to print or save




Fish - These patterns are based on a simple fish design, made of a tilted square with a triangle for a tail.
It's surprising how many ways you can fit these together.

Large grid of fish to print or save