Table of Contents
Tessellation
Tessellation – Explanation:
Tessellation is the process of creating a tessellation pattern. A tessellation pattern is a repeating geometric design that covers a plane without any gaps or overlaps. There are many different types of tessellations, but all of them share some common features.
The first step in creating a tessellation pattern is to choose a shape. You can use any shape you like, but it is easiest to start with a simple shape like a square or a rectangle. Next, you need to draw a grid on the plane where you want the tessellation to appear. The grid should be made up of squares or rectangles that are the same size as the shape you chose.
Now you can start to fill in the squares on the grid with the shape you chose. Be sure to make sure the shapes fit together perfectly, with no gaps or overlaps. If you need to, you can add in extra squares to the grid to help you keep the shapes aligned. When you are finished, the tessellation pattern should cover the entire plane.
Tessellation is the process of creating a repeating pattern of shapes within a flat surface. This can be done by using different shapes, colors, or sizes. Tessellations can be found in many different places, such as in nature, art, and architecture.
One of the most common places to find tessellations is in nature. The most famous example of this is the honeycomb. The honeycomb is made up of hexagons that repeat to create a honeycomb-like pattern. This pattern is very strong and efficient, which is why it is used in the construction of beehives.
Another common place to find tessellations is in art. One of the most famous examples of this is the quiltwork of Louise Nevelson. Nevelson used a variety of shapes and colors to create tessellating patterns in her quilts. These quilts are very colorful and eye-catching.
Finally, tessellations can also be found in architecture. One of the most famous examples of this is the Islamic architecture. The Islamic architects used a variety of shapes and patterns to create beautiful tessellating designs. These designs are often very intricate and complex.
Tessellations and The Way They are Utilized in Structure
Tessellations are a specific type of geometric pattern in which shapes are repeated in a regular fashion to form a unified whole. They can be used to create a wide variety of structures, both two-dimensional and three-dimensional. In two dimensions, tessellations can be used to create intricate patterns on floors, walls, or other surfaces. In three dimensions, they can be used to create a variety of shapes, including domes, vaults, and arches.
Early Records of Tessellations
- Tessellations have been around for centuries, with the earliest known examples dating back to the Islamic world in the 12th century. These early tessellations were typically simple geometric shapes, such as squares and hexagons, that were repeated to cover a given space.
- The use of tessellations continued to develop over the centuries, with artists and architects increasingly experimenting with more complex and intricate designs. In the early 20th century, Dutch artist M.C. Escher became particularly famous for his tessellated designs, which often incorporated optical illusions and intricate patterns.
- Today, tessellations are still used in a variety of applications, from tile patterns in architecture to designs on fabric and wallpaper. They are also commonly used in mathematics and computer graphics, where they can be used to create patterns and shapes that can be used in 3D modelling.
What are Tessellations?
Tessellations are patterns that repeat over and over again in a fixed shape.
Styles of Tessellations
There are six types of tessellations:
- Regular: These are tessellations in which all the tiles are the same shape and size.
- Semi-Regular: These are tessellations in which all the tiles are the same shape, but not necessarily the same size.
- Regular Polygons: These are tessellations in which all the tiles are regular polygons.
- Semi-Regular Polygons: These are tessellations in which all the tiles are regular polygons, but not necessarily the same size.
- Irregular: These are tessellations in which the tiles are not all the same shape or size.
- Tripod: These are tessellations in which three tiles of the same shape are used to form a single tessellation.
Types of Tessellation
There are three types of tessellation: Regular, Semi-Regular, and Random.
Regular Tessellation
A regular tessellation is a type of tessellation in which the shapes that make up the tessellation are all the same size and shape. The edges of each shape fit perfectly against the edges of the other shapes, forming a repeating pattern.
Semi-Regular Tessellation
A semi-regular tessellation is a type of tessellation in which the shapes that make up the tessellation are all the same size and shape, but the edges of the shapes do not fit perfectly against one another. There is some space between the shapes, but the pattern still repeats.
Random Tessellation
A random tessellation is a type of tessellation in which the shapes that make up the tessellation are all different sizes and shapes. The edges of the shapes do not fit perfectly against one another, and the pattern does not repeat.
Classifying Tessellations
There are many ways to classify tessellations. One way is by the type of shapes that make up the tessellation.
Regular Tessellations
A regular tessellation is made up of shapes that are all the same size and shape. The shapes are usually polygons, such as squares, triangles, or hexagons.
Irregular Tessellations
An irregular tessellation is made up of shapes that are not all the same size or shape. The shapes can be any type of shape, not just polygons.
Difference Between the Four Types of Tessellation
There is a big difference between the four types of tessellation. The first type is regular tessellation, which is when the tiles are all the same size and shape. The second type is quasi-regular tessellation, which is when the tiles are all the same size, but not all of the same shape. The third type is semi-regular tessellation, which is when the tiles are all the same size and shape, but not all of the same color. The fourth type is irregular tessellation, which is when the tiles are not all the same size or shape.
What are Keplerʼs Tessellations?
Keplerʼs Tessellations are a series of shapes that can be repeated to create a pattern. The shapes are named after Johannes Kepler, who created them in 1619.
What are Regular Tessellations?
Regular Tessellations are shapes that can be repeated over and over again in a pattern without any gaps.
Semi-Regular Tessellations
A semi-regular tessellation is a tessellation in which some of the tiles are the same shape, but are arranged in different ways.
Demi-Regular Tessellations
A demi-regular tessellation is a tessellation in which polygons that are not regular are used.
There are three types of demi-regular tessellations:
Semi-Regular Tessellations
A semi-regular tessellation is a tessellation in which polygons that are not regular are used, and the polygons are all the same shape.
There are three types of semi-regular tessellations:
Quadrilateral Tessellations
A quadrilateral tessellation is a tessellation in which polygons that are not regular are used, and the polygons are all different shapes.
There are three types of quadrilateral tessellations:
Triangle Tessellations
A triangle tessellation is a tessellation in which polygons that are not regular are used, and the polygons are all different shapes.
There is only one type of triangle tessellation.
Non-Regular Tessellations
There are non-regular tessellations. A good example is the Penrose tiling.
Other Types of Verbs
There are other types of verbs, such as modals and auxiliary verbs.
Modals are used to express levels of certainty or doubt about a statement. There are nine modals in English: can, could, may, might, must, ought, shall, should, will, and would.
Auxiliary verbs are used to form compound verb tenses, such as the present perfect and future perfect. There are three auxiliary verbs in English: have, do, and be.
Which Shapes are Conducive for Tessellation and Why?
A square, rectangle, and hexagon are conducive for tessellation because they are all polygons with straight sides and angles that are all the same size.
