Irregular Tessellations

An irregular tessellation is a pattern of shapes that fit together to completely cover a surface, but the shapes are not regular polygons. In other words, the shapes do not have equal sides and angles. This creates a more complex and diverse pattern compared to regular tessellations.

Study Guide:

1. What are tessellations?
   Tessellations are patterns of shapes that fit together without any gaps or overlaps to cover a surface. These patterns can be found in art, architecture, and nature.
2. What is an irregular tessellation?
   An irregular tessellation is a type of tessellation where the shapes are not regular polygons. They can be a combination of different shapes such as triangles, quadrilaterals, and other irregular polygons.
3. Examples of irregular tessellations:
   
   • A combination of triangles and hexagons
   • A mix of pentagons and squares
   • A pattern including octagons and trapezoids
4. Properties of irregular tessellations:
   
   • Irregular tessellations have a more complex and diverse pattern compared to regular tessellations.
   • The shapes in irregular tessellations do not have equal sides and angles, leading to a more varied and interesting design.
5. Creating irregular tessellations:
   
   • Irregular tessellations can be created by experimenting with different irregular shapes and arranging them in a way that allows them to fit together without any gaps or overlaps.
   • Artists and designers often use irregular tessellations to create visually striking patterns and designs.

In summary, irregular tessellations are an intriguing and complex type of pattern that involves irregular shapes fitting together to completely cover a surface. Understanding the properties and creation of irregular tessellations can lead to a deeper appreciation of the intricate patterns found in art and nature.