What is an Octahedron in Geometry?
In geometry, an octahedron is a polyhedron with eight faces. A regular octahedron is a Platonic solid composed of eight equilateral triangles, four of which meet at each vertex. A cube can be seen as a degenerate octahedron with all edges and angles equal. It is one of the five Platonic solids, and the only one with fewer than 5 faces.
Octahedra are usually portrayed as two square pyramids joined at the base. If you cut them along the plane that cuts through the middle of the edge connecting the two pyramids, you would get two identical tetrahedra. The word "octahedron" comes from the Greek words for "eight" and "face".
An octahedron has 8 faces, made up of 6 vertices and 12 edges. The faces are all equilateral triangles.
There are 6 vertices on an octahedron. 4 of them meet at each vertex.
Each face meets another at an edge. Therefore, there are 12 edges on an octahedron.
An octahedron can be described by its face-vertex configuration or F-V configuration. This is denoted as [3,4]. The 3 represents the 3 sides that each triangle has while the 4 means that there are 4 triangles meeting at each vertex.
Net of an Octahedron
If you were to flatten out or “unfold” the octahedron, you would get what’s called a net of the octahedral shape. This net consists of 2 squares and 4 equilateral triangles put together. All the edges connect to form this shape without any gaps or overlaps. You can see how this would look in the image below:
Duality in Octahedral Shape
(Octahedral and Cubical)
(Octahedral and Tetrahedral)
Just like any other polyhedral shape, there is duality between the octahedral shape and another shape. The first example of this duality is between the octahedral shape and the cubical shape. This can be seen in how they are related to each other geometrically as well as algebraically. The second example is between the octahedral shape and the tetrahedral shape which again can be seen in both a geometric and algebraic way. These relationships are explored in more depth below.
In conclusion, an octahedron is a polyhedral shape with 8 faces made up of 6 vertices and 12 edges. It gets its name from Greek words for “eight” and “face” because it has 8 triangular faces. It is one of the five platonic solids and can be seen as a degenerate form of a cube. Its dual shapes are the cubical shape and the tetrahedral shape. Finally, its net consists of 2 squares and 4 equilateral triangles.
What is the use of octahedron?
The octahedron shape has many uses. One example is that it can be used as a container since it has a large amount of space inside and its flat sides make it easier to stack multiple containers on top of each other. It is also used in the construction of certain molecules and crystals.
What are the features of octahedron?
The octahedron has 8 faces, 6 vertices, and 12 edges. The faces are all equilateral triangles and the vertices all meet at four faces.
Why is a octahedron called a octahedron?
The octahedron gets its name from the Greek words for "eight" and "face" because it has 8 triangular faces.
Is octahedron a prism or pyramid?
An octahedron is neither a prism nor a pyramid. It is its own polyhedral shape with 8 faces, 6 vertices, and 12 edges.