### 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?

### Paving Paths

How many different ways can I lay 10 paving slabs, each 2 foot by 1 foot, to make a path 2 foot wide and 10 foot long from my back door into my garden, without cutting any of the paving slabs?

### LOGO Challenge 5 - Patch

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

# Semi-regular Tessellations

##### Stage: 3 Challenge Level:

Regular tessellations use identical regular polygons to fill the plane. The vertices of each polygon must coincide with the vertices of other polygons.

You can produce exactly three regular tessellations:

Can you convince yourself that there are no more?

Semi-regular tessellations (or Archimedean tessellations) have two properties:
• They are formed by two or more types of regular polygon, each with the same side length
• Each vertex has the same pattern of polygons around it.
Here are two examples:

In the first, triangle, triangle, triangle, square, square {3, 3, 3, 4, 4} meet at each point.
In the second, triangle, hexagon, triangle, hexagon {3, 6, 3, 6} meet at each point.

Can you find all the semi-regular tessellations?

Can you show that you have found them all?

The interactivity below can be used to test your ideas.

Full Screen Version
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To help you when you are working away from the computer, click below for multiple copies of the different polygons. You can print them, cut them out and use them to test which polygons fit together: 3 4 5 6 8 9 10 12