Icosahedron

Do you need to calculate the area or volume of a icosahedron? Use our calculator and you can automatically obtain this data by simply entering the measure of one of the edges of this figure.

If you would also like to know the formula to use or download a template for build your own icosahedronRead on because we will tell you all about this geometric figure formed by 20 equilateral triangles.

What is an icosahedron

Icosahedron

A regular icosahedron is a regular polyhedron (geometric figure) consisting of 20 faces formed by equal equilateral triangles.

How many faces does an icosahedron have? How many vertices does an icosahedron have? These are the questions that always come up when we talk about this figure, so below you will find the main ones. properties of the icosahedron:

  • 20 sides
  • 12 vertices
  • 30 edges
  • 5 concurrent edges at a vertex.

Now that we know more about this regular figure, let's learn how to calculate its volume, area and perimeter from the length of one of its sides or edges.

Area of the icosahedron

Icosahedron

To calculate the area of the icosahedron we only need to know the length of one of its edges (one of the sides of the equilateral triangle) and apply the following mathematical formula:

Area icosahedron = 5 ⋅ √3 ⋅ a2

This formula can be easily deduced since we know how to calculate the area of a triangle equilateral through the following formula:

Formula for calculating the area of an equilateral triangle

Like the icosahedron has 2o equilateral trianglesWe simply have to multiply by 20 the surface of one of them and that's it. Below you have the complete demonstration:

Demonstration of the formula for the area of the icosahedron

Volume of the icosahedron

Now that we know how to calculate the area, we are going to learn how to calculate the volume of the icosahedron. We only have to solve the following formula:

Formula for calculating the volume of an icosahedron

 

Truncated Icosahedron

Truncated Icosahedron

You have probably heard of a truncated icosahedron and you have probably seen one on more than one occasion. Have you noticed how soccer balls are constructed? Well, they are a clear example of a truncated icosahedron.

They are formed by truncating (cutting) each vertex of an icosahedron.

This type of polyhedra consists of 32 sidesof which 12 are pentagons and 20 are hexagons. In this case, the number of edges increases to 90 and the number of vertices is 60.

With this polygon roundness is considerably improved of the figure although it does not achieve a perfect sphere but remains at almost 87% (86.74% to be exact). To improve it we have to add even more faces.

If you want to build your own truncated icosahedronbelow you have a template to develop it.

Truncated icosahedron template

You just have to print it, cut it out leaving some border to make the flap to apply glue and assemble it.

How to make an icosahedron

In case you want to build an original icosahedron, here is a template that will be very useful to understand how this figure looks like or simply to practice your origami skills.

Template icosahedron

Just trim the edges, fold the flaps and the area of broken lines. Then apply some glue where it says "glue under" and assemble the figure.

In a few minutes you will have your figure ready.

If you have any doubts or need to know more information about this regular polyhedron that we have not mentioned, leave us a comment and we will help you clear up your doubts.

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