How many different types of semi irregular tessellations are there?
I found it!!! ;-)
eight.
http://www.mathpuzzle.com/Tessel.htm
To determine the number of different types of semi-regular tessellations, we first need to understand what semi-regular tessellations are and how they differ from regular and irregular tessellations.
A tessellation is a pattern of shapes that perfectly covers a plane without any gaps or overlaps. In a regular tessellation, only one type of regular polygon (such as equilateral triangles, squares, or hexagons) is used, and the arrangement of these polygons is the same at every vertex. In contrast, an irregular tessellation uses different shapes and does not repeat the same arrangement of shapes at each vertex.
Semi-regular tessellations fall between regular and irregular tessellations. They are made up of two or more regular polygons, and the arrangement of these polygons varies at each vertex. However, they must still follow certain rules:
1. The same polygons must meet at each vertex.
2. The polygons must be arranged in a consistent pattern.
The six different types of semi-regular tessellations are also known as Archimedean tessellations. They are named after the Greek mathematician Archimedes, who first described them. The types of semi-regular tessellations are classified based on the combination of regular polygons used.
Here are the six types of semi-regular tessellations:
1. Triangles and squares (3.4.3.4)
2. Triangles and hexagons (3.6.3.6)
3. Triangles, squares, and hexagons (3.3.3.4.4)
4. Triangles and dodecagons (3.12.12)
5. Squares and octagons (4.8.8)
6. Hexagons and octagons (6.8.8)
Therefore, there are six different types of semi-regular tessellations, each characterized by a specific combination of regular polygons.