What is Dodecahedron?
The concept of the dodecahedron is based on a three-dimensional figure, and it has 12 complete faces, which make a pentagonal shape. The faces look like 2D shapes. Among the group of the five 2D faces, a dodecahedron is formed. The 2D solids look different, and these are essentially convex polyhedral where the faces are all constructed with congruent regular polygons having a similar number of faces all meeting at each other at a specific vertical.
Here the specific shape is designed with the 1w congruent pentagons, and the three pentagonal faces are made to meet each other at all the twenty vertices.
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The dodecahedrons come in two varieties: the usual and the unusual dodecahedrons. The term is derived from the Greek word “dodeka”. Here dodeka stands for 12, and the dodecahedron meaning is a 12-faced polygon. Hence, it is the kind of polyhedron with 12 sides and 12 faces. Thus, any particular polyhedral with all 12 sides can surely be termed as dodecahedrons. Based on the dodecahedron meaning, one can well understand the properties of the polyhedral.
The Net of Dodecahedron
For instance, one is made to live on one of the platonic solids, and you even have a house in the line of the vertices. However, you have neighbours living on the other vertices. Each morning when you are out jogging, you should run in a straight line. This will make you never change or turn the main path. At this point, it is important to go on a straight line, and then you can return back to your home destination without going by your neighbour’s house. This is how you get an idea about the dodecahedron net.
Over the last 2000 years, mathematicians had an idea about the dodecahedron net. In recent times there are the three most popular mathematicians with the name of Jayadev Athreya, David Aulicino, and Patrick Hooper. All three of them have discovered the specific solution as part of the dodecahedron puzzle. However, the shape has specific 31 diverse paths. The different dodecahedron nets will help us in identifying the faces, the vertices, and the edges. It is easy for you to shape your own dodecahedron and have fun with the shape.
Shaping the Net
It is all about the dodecahedron shape of which the net is a part. You can take a printout of the same and have an understanding of the dodecahedron netting system. For this, you have to fold the shape along the inside lines, and then you can glue the similar coloured lines to form a convex shape of the dodecahedron. This will help you have an idea of the regular and the simple dodecahedron in real life. In the usual case of a dodecahedron, there are twelve regular pentagonal sides.
Main Traits of the Shape
These are the main characteristics of a dodecahedron. This will let you learn about the properties like the edges, sides, shapes, angles, and vertices, all things related to the main regular dodecahedron concept and shape with the right specifications. The dodecahedron has twelve pentagonal sides. Moreover, the shape has all the distinct 30 edges, and it has a total of 20 vertices, and these are the specific corner points. The shape has the specific 160 diagonals, and the sums of the angles are just right for the purpose. It is all 3 x 108° = 324°.
The dodecahedrons are visible in real-life situations. You can take a look at the Roman dodecahedrons, and you even have the dice made on a similar concept. It is the part and purpose of dodecahedron to apply the set of tricks and tips for a better understanding of the concept. There is the shape of Icosahedron, and it is denoted as the dual of the dodecahedron, and both of them come with a similar number of edges in total.
FAQs on Dodecahedron
1) What is the definition of dodecahedron?
The dodecahedron is the shape with the complete 12 plane faces. The regular form of the shape is quite in vogue with the twelve actual pentagons as faces. This is quite usual in a platonic solid. You even have the three of the regular pentagons, just like the faces. These are constructed just like the stellations in the case of the convex form. All the shapes have icosahedral symmetry with the order of 120.
2) What are the properties and formulas of the dodecahedron?
The regular form of the shape is called pentagonal dodecahedrons. It consists of the twelve regular pentagonal faces and the specific three meeting points at each of the vertices. It is one of the five specific platonic solids and has all the 12 faces, the 20 vertices, and a total of 30 edges. There are 160 diagonals, among which 60 are the face diagonals, and 100 are the space diagonals. You have both forms of dodecahedrons, and these are regular and convex. All the faces meet at one vertex to create a complete shape.
3) What are the examples of a dodecahedron?
You have the small and the stellated dodecahedrons with the size of 5/2, 5, and there is also the greater dodecahedron, the measurement of which is 5/2, 3. The interesting and the right small-stellated dodecahedron and the great dodecahedron are quite dual to one another. The option of the great stellated dodecahedron is dual to the option of icosahedrons. The examples of dodecahedron can be passively used in the making of the regular mathematical shapes, and they even form a part of the unique design examples for that exceptional experience in specific.
