Tessellations with pattern blocks

1. Get acquainted with pattern blocks:
   
   What are the angles in each of the pieces?
   Which edges have he same lengths?
• square
• equilateral triangle
• regular hexagon
• trapezoid
• fat rhombus
• thin rhombus
2. Can you tessellate the plane with only one type of piece? (Answer for each type of piece.)
   For a given piece, can you tessellate in more than one way?
3. Some characteristics of tessellations: How can you describe the way(s) in which two tessellations are the same or different?
• Definition of an edge-to-edge tessellation: Endpoints only touch other endpoints. (You can't have an endpoint of one piece meeting the middle of another edge.)
• A tessellation is symmetric if each part of it is a repeat of another part. (This is not a specific enough definition; see a later page for precise definitions.)
4. Make an edge-to-edge tessellation. What is the sum of angles at a vertex? Check for several vertices.
5. Make a tessellation that is nvertices.
6. Make a tessellation that is not edge-to-edge. What can you say about the sum of angles at a vertex? Check for several vertices
7. How many different edge-to-edge tessellations are there that use
• just squares?
• just equilateral triangles?
• just regular hexagons?
• just fat rhombi?
• just thin rhombi?
• just trapezoids?
8. Is it possible to have one with a non-repeating pattern?
9. How can you be sure you have found all the possible tessellations?