$tessellation examples$

Consequently, the measure of their exterior angles is 0.įurthermore, observe that as the number of sides of the polygons increases, the fewer the number of vertices that we can fix at a common point without the polygons overlapping. Looking at the table in Figure 6, we can see that polygons whose product of interior angles and the number of adjacent vertices is 360 tessellate. It's surprising how many ways you can fit these together.Figure 6 – Table showing properties of tessellating and non-tessellating polygons. Here is a waffle pattern, and a suggested colour scheme.įish - These patterns are based on a simple fish design, made of a tilted square with a triangle for a tail. Waffle - You don't have to restrict yourself to regular shapes. Penrose tiles - these are based on five-fold symmetry, and they never repeat! (external site.) Large grid of irregular pentagons to print or save Pentagons - Regular pentagons won't make a tessellation, but rather squashed ones will. Large grid of dodecagons, hexagons and squares to print or save Large grid of dodecagons and triangles to print or save Large grid of octagons and squares to print or saveĭodecagons (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 hexagons, squares and triangles to print or save Large grids of triangles and hexagons to print or save - both types These tessellations can be made with triangle grids. Here, the hexagons are further apart, with a line of triangles between them. This packs the triangles closely, with a few triangles between. You can play around with the triangles grid to find other ways to mix hexagons and triangles. Hexagons and triangles - There are two regular ways to mix hexagons and triangles in the same pattern. Large grids of triangles and squares to print or save - both types The other grid looks strange, as we don't recognise squares as easily when they are tilted.

You can make it more interesting with colouring. Squares and triangles - There are two ways to mix squares and triangles in the same pattern. Hexagons can be made with triangle grids. Hexagons - Bees make natural tessellations of hexagons in their honeycombs. Make an Escher-style tessellation onlineĭesign an Escher-style tessellation onlineĭesign mosaics online - which you can use to make tessellations Click here to make a square tessellation online. Squares - rather obvious! By colouring them, you can build up more complicated patterns. Six triangles make a hexagon.ĭesign a triangle mosaic online - which you can use to make tessellations Triangles - these make pretty tessellations.

Large grid of dodecagons, hexagons and squares Large grid of hexagons, squares and triangles

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

Tessellation examples