Semiregular Tessellations

A tessellation is the tiling of a plane using one or more geometric shapes, with no overlaps and no gaps. A semiregular tessellation is a specific type of tessellation that uses two or more regular polygons in such a way that the same sequence of polygons meet at each vertex. In other words, the pattern of polygons around each vertex is the same throughout the tessellation. There are eight possible semiregular tessellations, which are also known as Archimedean tessellations.

Types of Semiregular Tessellations

There are eight types of semiregular tessellations, each defined by the combination of regular polygons used:

• Type 1: Triangles and hexagons
• Type 2: Squares and hexagons
• Type 3: Triangles and squares
• Type 4: Triangles, squares, and hexagons
• Type 5: Triangles and dodecagons
• Type 6: Triangles and squares
• Type 7: Triangles and hexagons
• Type 8: Triangles, squares, and hexagons

Properties of Semiregular Tessellations

Some important properties of semiregular tessellations include:

• Each vertex in a semiregular tessellation is surrounded by the same sequence of regular polygons.
• Each edge in a semiregular tessellation is shared by two regular polygons.
• There are no gaps or overlaps in a semiregular tessellation.
• The total angle around each vertex in a semiregular tessellation is 360 degrees.

Study Guide

If you're studying semiregular tessellations, here are some key points to focus on:

1. Understand the definition of a tessellation and the difference between regular and semiregular tessellations.
2. Learn the eight types of semiregular tessellations and the combinations of regular polygons they use.
3. Practice identifying and creating semiregular tessellations using paper, pencil, and geometric shapes.
4. Explore the properties of semiregular tessellations, such as the angles around each vertex and the sharing of edges between regular polygons.
5. Consider real-world examples of semiregular tessellations, such as in architecture, art, and design.

By mastering the concepts and properties of semiregular tessellations, you'll develop a deeper understanding of geometric patterns and their applications in various fields.