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Broad Topics > Transformations and constructions > Tessellations

Semi-regular Tessellations

Age 11 to 16 Challenge Level:

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

Gibraltar Geometry

Age 11 to 14 Challenge Level:

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

Polygon Rings

Age 11 to 14 Challenge Level:

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

L-triominoes

Age 14 to 16 Challenge Level:

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

Polygon Walk

Age 16 to 18 Challenge Level:

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

Tiles in a Public Building

Age 7 to 11 Challenge Level:

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

Tessellation Interactivity

Age 7 to 16 Challenge Level:

An environment that enables you to investigate tessellations of regular polygons

The Square Hole

Age 14 to 16 Challenge Level:

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

Equal Equilateral Triangles

Age 14 to 16 Challenge Level:

Using the interactivity, can you make a regular hexagon from yellow triangles the same size as a regular hexagon made from green triangles ?

Outside the Box

Age 7 to 14

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

Making Maths: Kites and Darts

Age 7 to 11 Challenge Level:

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

Tessellating Capitals

Age 5 to 7 Challenge Level:

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

Escher Tessellations

Age 7 to 11 Challenge Level:

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

Tessellating Transformations

Age 7 to 11 Challenge Level:

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?

Tessellating Hexagons

Age 11 to 14 Challenge Level:

Which hexagons tessellate?

Lafayette

Age 7 to 11 Challenge Level:

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

Maurits Cornelius Escher

Age 7 to 14

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. . . .

Shaping up with Tessellations

Age 7 to 14

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. . . .

Napoleon's Theorem

Age 14 to 18 Challenge Level:

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?

Shapely Tiling

Age 7 to 11 Challenge Level:

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?

Bow Tie

Age 11 to 14 Challenge Level:

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.

Schlafli Tessellations

Age 11 to 18 Challenge Level:

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. . . .

LOGO Challenge - Tilings

Age 11 to 16 Challenge Level:

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. . . .

LOGO Challenge - Triangles-squares-stars

Age 11 to 16 Challenge Level:

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.

LOGO Challenge 5 - Patch

Age 11 to 16 Challenge Level:

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

Building Stars

Age 7 to 11 Challenge Level:

An interactive activity for one to experiment with a tricky tessellation

Tetrafit

Age 7 to 11 Challenge Level:

A tetromino is made up of four squares joined edge to edge. Can this tetromino, together with 15 copies of itself, be used to cover an eight by eight chessboard?

Triominoes

Age 11 to 14 Challenge Level:

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. . . .

Two by One

Age 7 to 11 Challenge Level:

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

Tessellating Triangles

Age 7 to 11 Challenge Level:

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

Penta Place

Age 7 to 11 Challenge Level:

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