What is an OCTAHEDRON and its characteristics

An octahedron is a geometric shape made up of eight faces that take the form of polygons. This solid, known as a polyhedron, represents a three-dimensional figure that exhibits eight sides, or faces.

In a new lesson from a Teacher we will see what is an octahedron and its characteristics. First we will start with the concept of polygons and polyhedra. Then we will study the octahedron, its elements and its characteristics. We will also talk about the Platonic solids and the types of octahedrons that exist.

An octahedron is a geometric figure that is made up of eight faces. which are polygons The octahedron is a polyhedron, that is, a three-dimensional figure that has eight sides or faces.

Their faces can be formed by triangles, squares, pentagons, hexagons and heptagons. With this we can ensure that an octahedron can be formed with any polygon whose sides are less than eight.

If all the faces of an octahedron are equilateral triangles, then we can say that the octahedron it is regular.

This kind of figure

It is considered a Platonic solid. This is because Plato associates each of the elements that make up the Universe, that is, earth, air, water and fire, to a polyhedron. That is, fire is associated with the tetrahedron, water with the icosahedron, earth with the cube, and air with the octahedron. He also associated the Universe with the last solid that is the dodecahedron.

Octahedrons can be formed by eight polygons that are regular or irregular. Therefore, there are two types of octahedrons that are regular and truncated.

• regular octahedron: convex polyhedron that has eight faces that are triangles. Two of its faces are made up of isosceles triangles, while its other six faces are equilateral triangles. The shape of this polyhedron is symmetric, therefore all its angles will be equal.
• truncated octahedron: polyhedron with its eight irregular faces. Two of its faces are made up of hexagonal polygons, while its other six faces are made up of both straight lines and curved lines. The shape of this polyhedron is asymmetric, so its angles are not all equal.

The polygons are those geometric figures with a main characteristic: They are flat and closed. They are formed by a series of line segments, called "sides" that are joined together to build the figure.

The points that connect the different line segments are called verticesTherefore, the number of vertices of a figure will always be equal to the number of sides it has.

Polygons are named from the number of sides and vertices that the figure has. Let's look at some examples of the types of polygons:

• Triangle: polygon with three sides.
• Quadrilateral: polygon with four sides.
• Square: polygon with four equal sides and four right angles.
• Rectangle: polygon with four sides, one pair of equal opposite sides, and four right angles.
• trapezoid: polygon with four different sides, with no side parallel to another.
• Pentagon: polygon with five sides and five angles.
• Hexagon: polygon with six sides and six angles.
• Heptagon: polygon with seven sides and seven angles.
• Octagon: polygon with eight sides and eight angles.
• enneagon: polygon with nine sides and nine angles.
• Decagon: polygon with ten sides and ten angles.
• Hendecagon: polygon with eleven sides and eleven angles.
• Dodecagon: polygon with twelve sides and twelve angles.

The polyhedra are those geometric figures that have three dimensions and are made up of a known number of polygons called faces.

The main difference between polygons and polyhedra is that polygons are two-dimensional figures, that is, they are plane figures, while Polyhedrons are three-dimensional figures. that is, figures of space, which are also made up of polygons.

The polyhedrons then, are three-dimensional geometric figures, formed by faces that enclose a volume. As we mentioned with the polygons, depending on the number of faces they have, the polyhedra will have their different names. let's see some examples.

1. Parallelepiped: polyhedron formed by two regular squares and four equal rectangles.
2. Cube: polyhedron formed by six equal rectangles.
3. Pyramid: polyhedron formed by a base and several triangles.
4. Prism: polyhedron formed by parallelograms.
5. Octahedron: polyhedron formed by the union of two pyramids from its base.
6. Dodecahedron: polyhedron formed by twelve regular faces.