First, let us identify these five geometric objects — or, in the terminology of mathematicians, geometric solids.
First of all, why are these five geometric solids called regular polyhedra?
This is quite easy to remember. The sides of regular polyhedra are regular polygons. In turn, regular polygons are those in which all sides are equal (e.g., triangle, square) and have equal angles between adjacent sides. This is why they are called "regular".
What is the connection with Plato?
The ancient Greek scientist Plato was most likely not related to discovering these remarkable polyhedrons, but Plato had another talent. In the modern world, Plato could be called the popularizer of regular polyhedra. The greatest contribution Plato made is that he told people about the existence of regular polyhedra.
If this is all he had done, however, the majority would have quickly forgotten about them. But Plato endowed these seemingly simple objects with incredible strength and mystical meaning and brought them to the forefront of his teaching.
In an attempt to explain the nature of everything that exists, Plato considered five regular polyhedra to be fundamental principles for the structure of each of the elements:
- fire correlated with the tetrahedron;
- air correlated with the octahedron;
- earth correlated with the hexahedron;
- water correlated with icosahedron;
- and the dodecahedron corresponded to the Universe.
One can specify the following mathematical characteristics in each of the five Platonic solids: 1....