Tessellations

There are 32 NRICH Mathematical resources connected to Tessellations

problem

Favourite

Polygon rings

Age

11 to 14

Challenge level

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

problem

Favourite

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?

problem

Favourite

Cover the camel

Age

5 to 7

Challenge level

Can you cover the camel with these pieces?

problem

Favourite

Repeating patterns

Age

5 to 7

Challenge level

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

problem

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.

problem

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.

problem

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?

problem

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?

problem

Tessellating hexagons

Age

11 to 14

Challenge level

Which hexagons tessellate?

problem

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?

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For younger learners

Tessellations

Polygon rings

Semi-regular tessellations

Cover the camel

Repeating patterns

Schlafli tessellations

Bow tie

Shapely tiling

Napoleon's theorem

Tessellating hexagons

Tessellating transformations