Do you want to calculate the area or volume of a dodecahedron? Use our online calculator and you will be able to calculate the area of this 12-sided figure.
If you also want to know the formula to use, download a template to make your own dodecahedron and more data related to this polyhedron, read on.
What is a dodecahedron
A dodecahedron is a regular polyhedron which has a total of 12 faces formed by regular pentagons.
This last fact is something that we can deduce from its name since 'dodeca' es un prefijo que viene del griego y significa 12. Como ya imaginarás, 'edro' significa cara.
How many faces does a dodecahedron have? And how many vertices?
We have already seen in the previous point that the dodecahedron has 12 faces which are regular pentagons.
We can also say that the dodecahedron has 30 edges and a total of 20 vertices in which three edges coincide in each one.
Area of a dodecahedron
Now that we know what a dodecahedron is, let's learn how to calculate its area. We know that each face of the polyhedron is a pentagon and we know how to calculate the area of a pentagon regular.
Since the dodecahedron has 12 faces, we simply multiply by 12 the formula to calculate the area of the pentagon. In the end we are left with the following formula for calculating the area of a regular dodecahedron:
Demonstration of the formula for the area of a dodecahedron
If you want to know how the above formula has been obtained, let's see the demonstration. To do this we start from the formula for calculating the area of a regular pentagon which is as follows:
In this formula, L is the length of one side of the pentagon and ap is the apothem. which we will calculate with this other formula:
The next step is to put it all together. In other words, we will multiply by 12 the formula to calculate the area of a regular pentagon because the dodecahedron has 12 faces, furthermore, we will substitute the value of the apothem and we will be left with the following:
Volume of a dodecahedron
If what we want is calculate the volume of a dodecahedronIf the formula we have to apply is this other formula:
Siendo 'a' la longitud de uno de los lados o aristas del poliedro de 12 caras.
Template for building a dodecahedron
If you want to make your own dodecahedron, here is a template that you can print for its development:
Just print it on a sheet of paper and cut it out carefully following the outline marked by the lines.
Once you have cut out the dodecahedron template, fold the flaps and the dashed line area, then apply some glue to the flaps to proceed with the gluing process.
Allow a few minutes for the glue to take effect and then you will have the figure mounted so you can enjoy it in three dimensions.
If you want to have your own rubik's dodecahedron, you can get one in the link we just left you. It does not cost much and will test your skills to solve it.
This 12-sided rubik is more difficult than usual because not only do you have to make the faces have the same color, you also have to find the right size in each of them because as you can see in the image there are multiple divisions in each pentagon.
If you want to put yourself to the test, we recommend that you get one of these rubik.
If you want to build a stellated dodecahedron like the one in the image, download the following template and print it 3 times.
Once you have it printed, get the following material:
- Double-sided tape or glue
When you have everything done, follow the next step by step:
- On each sheet you have printed there are two shapes but we will need 5 to build the stellated dodecahedron. Cut them out.
- Now it's time to join the 5 shapes you just cut. You have to group them as shown in images 2 and 3 of the step by step. When you have them in place, start gluing the flaps.
- The next thing you need to do is to start creating the triangular stitches. To do this, fold along the marked lines. Help yourself with the ruler if necessary. At first it will be hard until you get the hang of it, but then it's very easy.
- Once you have made all the folds, apply the glue to the remaining flaps and that's it, you have your star-shaped dodecahedron.
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