If you are a board game lover then this shape might be familiar to you. Many board games use this geometrical figure as a dice. One thing is for sure and that is this figure is a polyhedron. Like other polyhedrons, octahedron has its own properties and that is why we dedicated this resource to the octahedron.

What is an Octahedron?

The word, "Octahedron" can be broken into two words, octa and hedron. The origin of both words is from ancient Greek. The word, "octa", means eight and the word, "hedron" means faces. Hence, octahedron means a polyhedron that contains eight faces. You might be wondering the shape of the face, is it rectangles? Or maybe squares? Actually, the shape of a face is triangular. Let's improve our definition, octahedron is a polyhedron that is composed of 8 triangles. Below is the shape of the octahedron.

The picture shows four faces, however, the octahedron contains eight faces, where are the other four? Then let us inform you, what you are looking at is a 2-dimensional image. Of course, the same shape is at the back of the figure hence, 4 + 4 = 8 faces, four on front and four on behind. Nevertheless, we wanted to talk about regular octahedrons.

Regular Octahedron

As the name tells you that the figure will be an octahedron but what is the difference between an octahedron and a regular octahedron? A regular octahedron is a regular polyhedron composed of 8 equal equilateral triangles. Hence, the only difference is that a regular octahedron will always have all dimensions equal but for an octahedron, it can have different dimensions. In addition, the regular octahedron can be considered to be formed by the union of two equally sized regular quadrangular pyramids at their bases.

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Unfold of a Regular Octahedron

The unfolding of a figure helps in understanding it more. For example, the unfolded figure can help in understanding its characteristics as well as it can help in calculating the surface area of the figure. Octahedron is no exception and that is why we will commence the unfolding of the figure.

The above picture is the unfolded figure of a regular octahedron. You could easily see how triangles are joined together to make this figure. It is proof that the faces of the octahedron are triangular.

Characteristics of a Octahedron

To understand the nature of an octahedron, you need to know its characteristics. Lucky for you, we collected all the important characteristics that you should know about octahedrons. The list of characteristics is below:

Number of faces: 8.

Number of vertices: 6.

Number of edges: 12.

Number of concurrent edges at a vertex: 4.

Surface Area of a Regular Octahedron

Calculating the surface area of a regular octahedron is tricky but at the Superprof, we make things easy for students. There is a formula for calculating the surface area of the octahedron. That formula was derived using the unfolded region of an octahedron. Below is the formula for the calculation of the surface area of a regular octahedron.

A = 2 \sqrt { 3 } { a }^{ 2 }

Where, is the edge of a regular octahedron.

Volume of a Regular Octahedron

The volume of a regular octahedron means the total space occupied by the whole 3-D figure. To find the volume of a regular octahedron, you can use the below formula:

V = \frac { \sqrt { 2 } }{ 3 } { a }^{ 3 }

Where, is the edge of a regular octahedron.

Example

Calculate the surface area and volume of an octahedron with an edge of 5 cm.

A = 2 \sqrt { 3 } \times { 5 }^{ 2 } = 86.60 { cm }^{ 2 }

V = \frac { \sqrt { 2 } }{ 3 } \times { 5 }^{ 3 } = 58.98 { cm }^{ 3 }

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Hamza

Hi! I am Hamza and I am from Pakistan. My hobbies are reading, writing and playing chess. Currently, I am a student enrolled in the Chemical Engineering Bachelor program.