# Polyominoes Exploration

From EscherMath

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

- 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.

- 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).
- What kind of symmetry does each of the triominoes have? (Rotational? What angle? Reflectional? How many lines of symmetry?)
- Both triominoes tessellate the plane. Show a tessellation for each of the triominoes.
- 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).
- What kinds of symmetry does each of the tetrominoes have? (Rotational? What angle? Reflectional? How many lines of symmetry?)
- All tetrominoes tessellate the plane. Show a tessellation for each of the tetrominoes.
- 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).
- 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.
- How many different tilings can you create using just the "long pentomino"?
- 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.