Tessellations

1. Tessellations Advanced Geometry Rigid Transformations Lesson 4

2. Symmetry Figures that are indistinguishable following a transformation have symmetry.

3. Tessellation pattern no overlapping or empty spaces on the right is not a tessellation but a pattern.

4. Tessellations repeat and have clearly defined closed shapes. Patterns repeat but do not have clearly defined closed shapes.

5. Regular Tessellation one type of REGULAR POLYGON Equilateral triangles Squares Regular hexagons

6. Uniform Tessellation the same arrangement of shapes and angles at each vertex

7. Semi-regular Tessellation uniform two or more regular polygons

8. Example: Determine whether each polygon tessellates the plane. If so, describe the tessellation as uniform, not uniform, regular, or semi-regular.

9. We must determine if certain polygons tessellate the plane. Look at the angle measures at each vertex to decide. The angles at every vertex must have a sum of EXACTLY 360°.

10. Angles of a Regular Polygon 180(n – 2) First find the sum of the angles of the polygon. n = # of angles Sum Then divide by the number of angles. n

11. Example: Determine whether a regular 16-gon tessellates the plane. Explain.

12. Example: Determine whether each polygon or set of polygons tessellates the plane. If so, describe the tessellation as uniform, not uniform, regular, or semi-regular.

13. Example: Determine whether a semi-regular tessellation can be created from each set of figures. Assume that each figure has side length of 1 unit. regular pentagon and square

14. Example: Determine whether a semi-regular tessellation can be created from each set of figures. Assume that each figure has side length of 1 unit. squares and equilateral triangles

15. Example: Stained glass is a very popular design selection for church and cathedral windows. Determine whether the pattern is a tessellation. If so, describe it as uniform, not uniform, regular, or semi-regular.