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There are **31** NRICH Mathematical resources connected to **Tessellations**, you may find related items under Transformations and constructions.

Problem
Primary curriculum
Secondary curriculum
### Polygon Rings

Join pentagons together edge to edge. Will they form a ring?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Repeating Patterns

Try continuing these patterns made from triangles. Can you create your own repeating pattern?

Age 5 to 7

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Semi-regular Tessellations

Semi-regular tessellations combine two or more different regular polygons to fill the plane. Can you find all the semi-regular tessellations?

Age 11 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Gibraltar Geometry

Take a look at the photos of tiles at a school in Gibraltar. What questions can you ask about them?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### L-triominoes

L triominoes can fit together to make larger versions of themselves. Is every size possible to make in this way?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Polygon Walk

Go on a vector walk and determine which points on the walk are closest to the origin.

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Tiles in a Public Building

What is the same and what is different about these tiling patterns and how do they contribute to the floor as a whole?

Age 7 to 11

Challenge Level

Interactive
Primary curriculum
Secondary curriculum
### Tessellation Interactivity

An environment that enables you to investigate tessellations of regular polygons

Age 7 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### The Square Hole

If the yellow equilateral triangle is taken as the unit for area, what size is the hole ?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Equal Equilateral Triangles

Can you make a regular hexagon from yellow triangles the same size as a regular hexagon made from green triangles ?

Age 14 to 16

Challenge Level

Article
Primary curriculum
Secondary curriculum
### Outside the Box

This article explores the links between maths, art and history, and suggests investigations that are enjoyable as well as challenging.

Age 7 to 14

General
Primary curriculum
Secondary curriculum
### Making Maths: Kites and Darts

Using these kite and dart templates, you could try to recreate part of Penrose's famous tessellation or design one yourself.

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Tessellating Capitals

Have you ever tried tessellating capital letters? Have a look at these examples and then try some for yourself.

Age 5 to 7

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Escher Tessellations

This practical investigation invites you to make tessellating shapes in a similar way to the artist Escher.

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Tessellating Transformations

Can you find out how the 6-triangle shape is transformed in these tessellations? Will the tessellations go on for ever? Why or why not?

Age 7 to 11

Challenge Level

General
Primary curriculum
Secondary curriculum
### Lafayette

What mathematical words can be used to describe this floor covering? How many different shapes can you see inside this photograph?

Age 7 to 11

Challenge Level

Article
Primary curriculum
Secondary curriculum
### Maurits Cornelius Escher

Have you ever noticed how mathematical ideas are often used in patterns that we see all around us? This article describes the life of Escher who was a passionate believer that maths and art can be intertwined.

Age 7 to 14

Article
Primary curriculum
Secondary curriculum
### Shaping up with Tessellations

This article describes the scope for practical exploration of tessellations both in and out of the classroom. It seems a golden opportunity to link art with maths, allowing the creative side of your children to take over.

Age 7 to 14

Problem
Primary curriculum
Secondary curriculum
### Napoleon's Theorem

Triangle ABC has equilateral triangles drawn on its edges. Points P, Q and R are the centres of the equilateral triangles. What can you prove about the triangle PQR?

Age 14 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Shapely Tiling

Use the interactivity to make this Islamic star and cross design. Can you produce a tessellation of regular octagons with two different types of triangle?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Bow Tie

Show how this pentagonal tile can be used to tile the plane and describe the transformations which map this pentagon to its images in the tiling.

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Schlafli Tessellations

are somewhat mundane they do pose a demanding challenge in terms of 'elegant' LOGO procedures. This problem considers the eight semi-regular tessellations which pose a demanding challenge in terms of 'elegant' LOGO procedures.

Age 11 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### LOGO Challenge - Tilings

Three examples of particular tilings of the plane, namely those where - NOT all corners of the tile are vertices of the tiling. You might like to produce an elegant program to replicate one or all of these.

Age 11 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### LOGO Challenge - Triangles-squares-stars

Can you recreate these designs? What are the basic units? What movement is required between each unit? Some elegant use of procedures will help - variables not essential.

Age 11 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### LOGO Challenge 5 - Patch

Using LOGO, can you construct elegant procedures that will draw this family of 'floor coverings'?

Age 11 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Triominoes

A triomino is a flat L shape made from 3 square tiles. A chess board is marked into squares the same size as the tiles and just one square, anywhere on the board, is coloured red. Can you cover the board with trionimoes so that only the square is exposed?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Two by One

An activity making various patterns with 2 x 1 rectangular tiles.

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Tessellating Triangles

Can you make these equilateral triangles fit together to cover the paper without any gaps between them? Can you tessellate isosceles triangles?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Penta Place

Penta people, the Pentominoes, always build their houses from five square rooms. I wonder how many different Penta homes you can create?

Age 7 to 11

Challenge Level