Tessellations

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

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

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

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

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

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

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?

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

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

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.