In geometry, a dodecahedron is a body composed of 12 convex faces, 30 edges, and 20 vertices. This body is one of the most harmonious and independent of the Platonic solids, since according to Plato it symbolized the universe. In order to calculate the total of the entire area of a dodecahedron, it is necessary to keep in mind the area of the pentagon, which is obtained through the following formula:
A = (a * P) / 2
Where "a" means the measure of the apothem of the pentagon and "p" represents the perimeter of the pentagon. Once the area of the pentagon is calculated, you just need to multiply by 12 (which is the pentagonal faces of the dodecahedron).
Now, when the dodecahedron has faces with regular pentagons, the dodecahedron is said to be regular. An example would be the case of the dice they use for role-playing games, these represent a regular dodecahedron. Each face is identified with a number:
The number 1 represents the smallest figure and which is opposite, to the face represented by the number 12, which is the largest figure. In fact, if both opposite figures are added, the result will be 13.
There are various kinds of dodecahedra, some of them are:
The blunt dodecahedron: they are those that belong to the group of the “Archimedean solids” (set of convex polyhedra with faces that are regular polygons of various types. Another of its characteristics is that it is convex and has uniform vertices.
The truncated dodecahedron: it also belongs to the group of "Archimedean solids", in order to obtain it, it is necessary to cut each vertex of a dodecahedron.
The tri-augmented dodecahedron: those of this type belong to the group of "Johnson solids" (polyhedron strictly convex).
