Tessellations

There are 32 NRICH Mathematical resources connected to Tessellations
Polygon Rings
problem
Favourite

Polygon rings

Age
11 to 14
Challenge level
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Join pentagons together edge to edge. Will they form a ring?

Semi-regular Tessellations
problem
Favourite

Semi-regular tessellations

Age
11 to 16
Challenge level
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Semi-regular tessellations combine two or more different regular polygons to fill the plane. Can you find all the semi-regular tessellations?

Cover the Camel
problem
Favourite

Cover the camel

Age
5 to 7
Challenge level
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Can you cover the camel with these pieces?
Repeating Patterns
problem
Favourite

Repeating patterns

Age
5 to 7
Challenge level
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Try continuing these patterns made from triangles. Can you create your own repeating pattern?
LOGO Challenge 5 - Patch
problem

Logo challenge 5 - patch

Age
11 to 16
Challenge level
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Using LOGO, can you construct elegant procedures that will draw this family of 'floor coverings'?
Tiles in a public building
problem

Tiles in a public building

Age
7 to 11
Challenge level
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What is the same and what is different about these tiling patterns and how do they contribute to the floor as a whole?
LOGO Challenge - Triangles-Squares-Stars
problem

Logo challenge - triangles-squares-stars

Age
11 to 16
Challenge level
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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.
Polygon walk
problem

Polygon walk

Age
16 to 18
Challenge level
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Go on a vector walk and determine which points on the walk are closest to the origin.
LOGO Challenge - Tilings
problem

Logo challenge - tilings

Age
11 to 16
Challenge level
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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.
L-triominoes
problem

L-triominoes

Age
14 to 16
Challenge level
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L triominoes can fit together to make larger versions of themselves. Is every size possible to make in this way?