# Pattern Block Exploration

From EscherMath

**Objective:**
Gain familiarity with regular polygon tessellations of the plane.

**Materials needed**: Pattern blocks. There are a number of "virtual pattern blocks" applets on the web. One of the best
is here [1].

In this exploration, "touch" means to share an edge. Corner touches don’t count.

- Warm up by making the three regular tessellations.
- Make some tessellations using combinations of triangles and squares:
- Can you make one so that no square touches another square?
- Can you make one so that each square touches exactly one other square?
- Can you make one so that each square touches exactly two other squares?
- Can you make one so that each square touches exactly three other squares?

- Can you make a tessellation using only hexagons and squares?
- Make some tessellations using combinations of triangles, squares, and hexagons:
- Can you make one so that no shape touches another block of the same shape? (This also means no tiles of the same color touch.)
- Can you make one so that no square touches a hexagon?

- Make more tessellations using all the tiles.

**Handin:**
A sheet with answers to all questions.