Tessellations

A tessellation is a pattern of shapes that fit together without any gaps or overlaps. The shapes can be simple, such as triangles, squares, or hexagons, or they can be more complex. Tessellations are found in many places in the world, including in art, architecture, and nature.

Types of Tessellations

There are three main types of tessellations:

1. Regular Tessellations: These are made up of one type of regular polygon, such as equilateral triangles, squares, or hexagons.
2. Semiregular Tessellations: These are made up of two or more regular polygons that meet at each vertex.
3. Irregular Tessellations: These are made up of irregular shapes that fit together without any gaps or overlaps.

Study Guide

To understand and work with tessellations, it's important to grasp the following concepts:

1. Regular Polygons: Understand the properties of regular polygons, such as the interior angles and the number of sides.
2. Transformational Geometry: Learn about translations, rotations, and reflections, as these are the techniques used to create tessellations.
3. Polyhedra: Understand the properties of 3D shapes that can be used to create tessellations in 3D space.
4. Art and Architecture: Explore examples of tessellations in art and architecture to understand how they are used in real-world applications.

Practice Problems

Here are some practice problems to help you master the concept of tessellations:

1. Create a tessellation using equilateral triangles.
2. Identify the type of tessellation (regular, semiregular, or irregular) for a given pattern.
3. Explore the symmetrical properties of tessellations using transformational geometry techniques.
4. Create a 3D tessellation using polyhedral shapes.

[Tessellations] Related Worksheets and Study Guides:

• Area and PerimeterMathematics • Fourth Grade