Polyominoes Exploration

Objective: Exploring Tessellations made from polygons creaed by combining squares of the same size. Topic is important for education majors.

The five free tetrominoes, top to bottom I, O, Z, T, L, marked with light and dark squares.

• A polyomino is a polygon made from squares of the same size, connected only along complete edges.

Examples:

• A triomino is a polyomino made from three squares.
• A tetromino is a polyomino made from four squares. Another name for a tetromino is a quadromino. Anyone who has ever played tetris will be familiar with these objects.
• A pentomino is a polyomino made from five squares.

1. There are exactly two triominoes. Draw both of them. (Two triominoes are considered the same if one can be obtained from the other by rotation or reflection).
2. What kind of symmetry does each of the triominoes have? (Rotational? What angle? Reflectional? How many lines of symmetry?)
3. Both triominoes tessellate the plane. Show a tessellation for each of the triominoes.
4. There are five different tetrominoes. Draw them. (Two tetrominoes are considered the same if one can be obtained from the other by rotation or reflection).
5. What kinds of symmetry does each of the tetrominoes have? (Rotational? What angle? Reflectional? How many lines of symmetry?)
6. All tetrominoes tessellate the plane. Show a tessellation for each of the tetrominoes.
7. There are twelve different pentominoes. Draw them. (Two pentominoes are considered the same if one can be obtained from the other by rotation or reflection).
8. Pick five of the pentominoes that you found and for each individual pentomino draw at least one tiling pattern that can be developed with it.
9. How many different tilings can you create using just the "long pentomino"?
10. Which of the pentomino shapes can be folded up into a cube (or more precisely, a box withoud a lid)?

Handin: A sheet with answers to all questions.