An octahedron is a polyhedron that has eight faces or planes.
Octahedron is a concept used in geometry to refer to a body that has eight planes or faces . The concept derives from the Latin octahedros , although its most distant etymological antecedent is found in the Greek language.
Octahedra are part of the group of polyhedra , which are those geometric bodies with a volume that is not infinite and that have flat faces. Because the octahedron has eight faces, it can be either a concave polyhedron or a convex polyhedron .
Characteristics of octahedra
One of the characteristics of octahedra is that each of its faces is a polygon that has, at most, seven sides. When all the faces of this geometric body are triangles classified as equilateral , we speak of a regular octahedron .
Regarding the properties of the octahedron, it is possible to point out that it has three axes of symmetry. Axes of symmetry are imaginary reference lines that, when dividing a given shape into two halves, cause the opposite points of the shape to be equidistant from each other, resulting in a symmetrical appearance. In the field of geometry, this concept refers to plane axes (every regular polygon has the same number of plane axes of symmetry as sides) and axial symmetry (a line that does not produce any change in the figures that rotate through it). around).
In addition to these lines, which join the opposite vertices of the octahedron, these figures also have six axes of symmetry of order two, which connect the centers of the opposite edges, and four of order three, lines that unite the barycenters of the faces. opposite. On the other hand, there are its nine planes of symmetry, three of which include the groups of coplanar edges, with the remaining six, perpendicular, containing the pairs of parallel edges.
Likewise, the octahedron has a center of symmetry , which makes its total order of symmetry 72 (this results from multiplying by two the sum of 3 axes x order 4 , 6 axes x order 2 and 4 axes x order 3 ). According to Schöenflies' notation, the aforementioned symmetry elements give rise to an octahedral symmetry group called O h ( O sub h ).
Role-playing game dice are usually octahedrons.
Different peculiarities
The conjugate polyhedron of the octahedron is a cube . This concept, also known as dual polyhedron , belongs to the field of geometry and refers to two polyhedra in which the vertices of the first coincide with the center of the faces of the second.
A particular property of the octahedron is that if a plane passes through the center of six of its edges and cuts it, the result is a regular hexagon.
The octahedron in different areas
We can find octahedrons in nature , since various crystals acquire this shape. Diamond , for example, is a mineral whose crystals can exhibit these characteristics. In the field of role-playing games , we can also find dice that have eight sides and are therefore octahedrons.
The figure of the octahedron is also very popular as an ornamental element, and can be easily constructed with paper , something that is also very useful for geometry students, to visually analyze its properties and characteristics. Assembling a homemade octahedron is relatively simple, since it simply consists of drawing a mold like the one seen in the image on the right, folding it properly and carefully gluing its flaps.
Octaedro , finally, is the name of a publishing house founded in 1992 in the city of Barcelona and of an Ecuadorian foundation that was born in 1995 to promote science and art .