What do you call a shape that has not one, not two, but 20 equal sides? The answer is more complicated than you might think. While your first inclination might be to call it a 20-sided polygon, it actually has a more formal name that is typically reserved for shapes with even more sides. Still, it never hurts to learn a new word or two, especially when it comes to something as beautiful and complex as geometry. So what is a 20-sided shape called, exactly? Let’s dive a little deeper.
As it turns out, a 20-sided shape is technically known as an icosagon. This term comes from the Greek word “eikosi,” which means “twenty,” and “gonia,” which means “angle.” So an icosagon is a polygon with 20 angles and 20 sides, all of which are equal in length. Of course, you’re not likely to come across an icosagon in your everyday life – they’re mostly used in advanced mathematics and geometry – but it’s still a fascinating bit of trivia to know.
So why bother learning about shapes like icosagons and other obscure polygons? For one thing, it’s always good to expand your knowledge and challenge yourself intellectually. Beyond that, though, understanding the intricacies of geometry can help you better understand the world around you. From the pattern of a honeycomb to the shape of a snowflake, geometry is all around us in both the natural and man-made world. And who knows – maybe the next time you encounter a 20-sided shape, you’ll be able to impress your friends with your newfound knowledge of what it’s called.
Polygons with More Than 10 Sides
Polygons are two-dimensional closed figures with straight sides. They consist of three or more sides and angles that add up to 180 degrees. Polygons are classified by the number of sides they have. A 20-sided polygon is called an Icosagon.
- Triacontagon: a polygon with 30 sides
- Tetracontagon: a polygon with 40 sides
- Pentacontagon: a polygon with 50 sides
Polygons with more than 10 sides are not commonly found in everyday life. However, they are frequently used in mathematics, design, architecture, and art. The study of these shapes is essential in fields such as geometry and trigonometry.
The number of sides of a polygon influences its properties and looks. For instance, polygons with an odd number of sides have one side more than their corresponding even-sided equivalent. As the number of sides increase, the angles of the polygon get closer and closer to 180 degrees. As a result, polygons with many sides look rounder or more circular.
| Number of Sides | Name | Interior Angles |
|---|---|---|
| 12 | Dodecagon | 1500° |
| 15 | Pentadecagon | 2340° |
| 20 | Icosagon | 3240° |
| 30 | Triacontagon | 5220° |
Understanding polygons and their properties, including those with many sides, is useful in many fields. From designing buildings to developing mobile apps, the knowledge of how to work with these shapes is essential for creating beautiful and functional structures and applications.
Regular vs Irregular Polygons
As we delve deeper into the world of geometry, we encounter an interesting concept: polygons. Put simply, polygons are closed shapes composed of straight lines. These shapes can have any number of sides, but we are particularly interested in the 20-sided polygon. So, what is a 20 sided shape called? This polygon is known as an icosagon.
Regular vs Irregular Polygons
- Regular polygons: These are polygons that have equal length sides and equal angles between those sides. Examples include the equilateral triangle, square, and hexagon.
- Irregular polygons: These polygons have sides and angles of varying length and size. An example of an irregular polygon is the kite shape.
When dealing with icosagons, it is important to understand whether you are working with a regular or irregular polygon. This distinction will dictate the properties and formulas you will use in your calculations.
Properties of Regular Icosagons
A regular icosagon has the following properties:
Interior angles: Each interior angle of a regular icosagon measures 162 degrees.
Exterior angles: Each exterior angle of a regular icosagon measures 18 degrees.
Perimeter: To calculate the perimeter of an icosagon, simply multiply the length of one side by 20.
Apothem: The apothem is the distance from the center of the icosagon to the midpoint of any side. In a regular icosagon, this value is equal to the square root of 5 minus 1 times the side length, all divided by 4.
Properties of Irregular Icosagons
An irregular icosagon does not have uniform side lengths or angles. This makes it more challenging to calculate its properties than its regular counterpart.
| Properties of Irregular Icosagons | |
|---|---|
| Interior angles: | The sum of the interior angles of an irregular icosagon is equal to (20 – 2) x 180 degrees, or 3240 degrees. |
| Perimeter: | To calculate the perimeter of an irregular icosagon, you must add up all of the side lengths. |
| Area: | The area of an irregular icosagon can be calculated using various methods, including dividing the polygon into triangles and using trigonometry to calculate each triangle’s area. |
As you can see, there are many differences between regular and irregular polygons. It is important to know which one you are working with in order to accurately calculate its properties and apply them in real-world situations.
Naming Polygons Based on Number of Sides
At some point in our lives, we’ve all learned about basic shapes like squares, circles, and triangles. These simple shapes are great for young children learning about geometry, but what about more complex shapes with a higher number of sides? Naming polygons based on the number of sides they have can be a little overwhelming, especially as the number of sides increases. In this article, we’ll discuss the various names for polygons based on the number of sides they possess.
Three-Sided Polygons
- Triangular: A three-sided polygon is called a triangular. It’s the simplest type of polygon that has a name. Triangulars appear everywhere in nature, from the shapes of the cells in your body to the structure of many crystals.
There are several types of triangulars:
| Triangle Type | Description | Picture |
|---|---|---|
| Equilateral Triangle | All sides are equal |  |
| Isosceles Triangle | Two sides are equal |  |
| Scalene Triangle | No sides are equal |  |
Now that we’ve covered three-sided polygons, let’s move on to polygons with more sides.
Properties of 20-Sided Polygons
A polygon is a closed two-dimensional shape with straight sides. A 20-sided polygon is called an icosagon. In this article, we will discuss the properties of 20-sided polygons, including their angles, sides, and area.
Angles of a 20-Sided Polygon
- The sum of the interior angles of a 20-sided polygon is 3240 degrees.
- Each angle in a regular 20-sided polygon measures 162 degrees.
- Each angle in an irregular 20-sided polygon can have a different measure.
Sides of a 20-Sided Polygon
A 20-sided polygon has 20 sides of equal line segments. In a regular 20-sided polygon, each side has the same length. In an irregular 20-sided polygon, the lengths of the sides can vary.
Area of a 20-Sided Polygon
The area of a 20-sided polygon can be calculated using the formula:
Area = (s² × n) / 4 × tan(π/n)
Where s is the length of one side, n is the number of sides, and π is pi (approximately 3.14159265359).
| Regular Icosagon | Irregular Icosagon |
|---|---|
| Each side has equal length | Sides can have different lengths |
| All angles have the same measure | Angles can have different measures |
| Symmetrical | Not symmetrical |
In conclusion, the 20-sided polygon, or icosagon, has unique properties that differentiate it from other polygons. Its angles, sides, and area can be calculated using specific formulas and measurements. By understanding these properties, we can better appreciate the complexity and beauty of geometry.
3D Shapes with 20 Faces
When it comes to 3D shapes with 20 faces, there are only two examples: the icosahedron and the dodecahedron. These shapes are classified based on their number of faces, edges, and vertices. The icosahedron has 20 equilateral triangle faces, 30 edges, and 12 vertices, while the dodecahedron has 12 regular pentagonal faces, 30 edges, and 20 vertices.
- Icosahedron: The icosahedron is a beautiful, symmetrical object that has 20 identical faces shaped like equilateral triangles. This shape is commonly used in dice, building blocks, and even sports balls like soccer balls.
- Dodecahedron: The dodecahedron is another interesting shape with 12 regular pentagonal faces. This shape is often used in crystal structures and geodesic domes.
Both the icosahedron and the dodecahedron have been studied extensively by mathematicians and scientists due to their unique properties and symmetry. They have also been used in various fields such as architecture, physics, and even art.
One interesting fact about the icosahedron and dodecahedron is that they are duals of each other. This means that if you connect the center of each face of one shape, you will get the other shape. The icosahedron and dodecahedron also have a close relationship to the Golden Ratio, a mathematical concept that has been used in art and design for centuries.
| Shape | Number of Faces | Number of Edges | Number of Vertices |
|---|---|---|---|
| Icosahedron | 20 | 30 | 12 |
| Dodecahedron | 12 | 30 | 20 |
In conclusion, 3D shapes with 20 faces are limited to only two types: the icosahedron and dodecahedron. These shapes not only have unique properties and symmetry, but they also have practical applications in various fields. Studying these shapes can give us a better understanding of geometry, mathematics, and the world around us.
Practical Applications of 20-Sided Shapes
When we think of shapes, squares and circles often come to mind as the most common and practical shapes. However, there are many other shapes that have their own unique uses and purposes. The 20-sided shape, also known as the icosagon, is one such shape that can be found in various practical applications.
Number 6: Uses in Board Games
One of the most popular practical applications of 20-sided shapes is in board games. The 20-sided die is a common component in many role-playing games where it is used to determine outcomes of actions and events. For example, in the game Dungeons and Dragons, players roll the 20-sided die to determine the success or failure of their character’s actions such as attacking an enemy or casting a spell.
- Role-playing games
- Board games that involve chance and risk
- Tabletop games
However, the use of 20-sided dice is not limited to fantasy role-playing games. It is also used in various board games that involve chance and risk. For instance, games like Risk and Settlers of Catan also use 20-sided dice to add randomness to the game. Additionally, 20-sided dice can also be used in tabletop games for strategy and combat simulations.
To further demonstrate the use of 20-sided shapes in board games, below is a table of some notable games that use the 20-sided die:
| Game | Number of 20-sided Dice |
|---|---|
| Dungeons and Dragons | Multiple |
| Risk | 1 |
| Settlers of Catan | 2 |
In conclusion, while the 20-sided shape may not be one of the most commonly used shapes in everyday life, it proves to be an essential component in various practical applications such as board games. Its random nature makes it a great tool for adding unpredictability and chance in various games and simulations.
Constructing a 20-Sided Polygon with a Compass and Straightedge
If you’re wondering what a 20-sided polygon is called, it’s a icosagon. Constructing an icosagon may seem like a daunting task, but it’s actually quite simple if you have the right tools and follow the correct steps.
- First, draw a circle with your compass.
- Next, mark points along the circumference of the circle at equal distances apart. To do this, use your compass to divide the circle into 20 equal parts.
- Starting at one of the marked points, use your straightedge to draw a line to the third marked point to the right.
- Then, draw a line from that third point straight up to the ninth point to the right.
- Continue this pattern until you have drawn all 20 lines.
- Finally, connect the end of the last line to the starting point to complete the icosagon.
It’s important to note that constructing an icosagon with a compass and straightedge requires precision and patience. Take your time and double-check your measurements before drawing each line. Once you have completed your icosagon, you’ll have a beautiful and unique shape that not many people know how to create.
Here is an example of how to divide the circle into 20 equal parts:
| Step | Action | Image |
| 1 | Draw a circle with your compass. |  |
| 2 | Place your compass on the circle’s center point and mark the circumference at equal distances apart. Do this 20 times around the circle. |  |
| 3 | Connect the marks to form the icosagon. |  |
With a bit of practice, constructing a 20-sided polygon with a compass and straightedge can become a fun and rewarding activity. Not only will you impress others with your geometric skills, but you’ll also have a newfound appreciation for the beauty and complexity of shapes.
What is a 20 sided shape called? FAQs
1. What is a 20 sided shape called in geometry?
In geometry, a 20 sided shape is called an icosagon.
2. How many sides does an icosagon have?
An icosagon has 20 sides, 20 vertices, and 30 edges.
3. What are some other names for a 20 sided shape?
Besides icosagon, a 20 sided shape is sometimes called a 20-gon or a regular icosagon.
4. Can an icosagon be a regular polygon?
Yes, an icosagon can be a regular polygon if all its sides and angles are equal.
5. Is an icosagon a common shape in real life?
No, an icosagon is not a common shape in real life. However, it can be found in some art forms or in architecture.
6. How do you calculate the area of an icosagon?
To calculate the area of an icosagon, you need to know the length of its apothem (the distance from the center to the midpoint of a side) and the length of its sides. The formula is Area = (1/2) x apothem x perimeter.
7. Why are there shapes with so many sides?
The reason for creating shapes with a large number of sides, like icosagons, is mainly for mathematical and geometrical exploration. It helps to study and formulate principles that can be applied in various fields like architecture, engineering, astronomy, and more.
Closing Thoughts
Thanks for taking the time to learn about what a 20 sided shape is called. Remember, an icosagon is a unique and intriguing shape that has its place in geometry and mathematics. Although it might not be a common shape in daily life, it’s still worth exploring its properties and what it can teach us. See you soon for more informative articles.