Polyhedra are those geometric elements with different flat faces. In fact, the word polyhedron in Greek literally means "many faces."
These figures can be understood as a solid or three-dimensional body and their volume depends on the different faces of each polyhedron.
It should be noted that the idea of a polyhedron refers to a set of polygons in three dimensions and the idea of a polygon refers to plane figures.
The decahedron is a ten-sided polyhedron
Polyhedra are regular when their different faces and angles are equal to each other and they are irregular when this criterion is not followed. Another way to classify them is by the number of faces. On the other hand, polyhedra are divided into convex and concave, the former being those that can be supported on all their faces, while the latter are those that do not have this property.
In this way, a ten-sided polyhedron is a decahedron. In other words, it is a geometric body made up of ten flat surfaces, but it is not a regular polyhedron since their faces are not all the same. At the same time, it is a polyhedron that can be both concave and convex, since the number of edges and vertices can vary.
As for the term decahedron, it is composed of two Greek roots: deka, which means ten and hedra, which means seat.
Examples of decahedra
In the role-playing game, a very original type of dice is used, as it has ten faces instead of the traditional six. This ten-sided die is also known by another name, a pentagonal trapezohedron (it is made up of 10 faces and four vertices on each of them).
A pentagonal bipyramid is made up of 10 equilateral triangles, 15 edges, and 7 vertices. This polyhedron allows us to explain the molecular structure or the three-dimensional arrangement of some atoms that make up a molecule.
Other examples of decahedra are the octagonal prism (10 faces, 24 edges and 16 vertices) or the enneagonal pyramid (10 faces, 18 edges and 10 vertices).
Plato and the polyhedra (the Platonic solids)
Plato was the first philosopher and mathematician to address the subject of polyhedra. According to this Greek philosopher of the lV century BC. C, each of the four elements that make up the universe (air, water, earth and fire) is associated with a different polyhedron. Fire is made up of tetrahedra, air is made up of octahedra, water is made up of icosahedra, and earth is made up of cubes.
It should be noted that for Plato there is a fifth polyhedral form, the dodecahedron, which has been used by God to establish the limit of the universe.
The vision of the Platonic solids expresses a double dimension: the structure of everything that exists and, in parallel, its beauty.
Photo: Fotolia - grandeduc
