You Polihedrons are geometric solids whose sides, called faces, are formed by polygons.. By limiting the faces, we have the edges and, in the encounter of these, there is the occurrence of the vertices. If a polyhedron meets the following classifications, it will be called a convex polyhedron:
The) two distinct faces that do not belong to the same plane;
B) each edge belongs to only two faces;
ç) the faces are formed by flat polygons;
d) the plane of each face leaves the entire solid in half space.
But there is a special classification of polyhedra called polyhedra of Plato or Plato's solids. In order for it to be a Plato's polyhedron, the polyhedron must comply with the following provisions:
The) all faces must have the same amount no of edges;
B) all vertices must be formed by the same amount. m of edges;
ç) The Euler's relationship must be: V - A + F = 2, on what V is the number of vertices, THE is the number of edges and F is the number of faces.
Mind Map: Plato's Polyhedra
*To download the mind map in PDF, Click here!
One convex polyhedron is said one regular polyhedron only if is a Plato's polyhedron and also if all its faces are formed by regular identical polygons. So we can say that a regular polyhedron is a Plato's polyhedron, but not the reciprocal.
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only exist five types of geometric solids that can be classified as Plato's polyhedra are:
O tetrahedron, O octahedron it's the regular icosahedron → have triangular faces;
The tetrahedron, octahedron and icosahedron are Plato's polyhedra with triangular faces
O regular hexahedron → polyhedron with square faces;
The hexahedron is Plato's only polyhedron with square faces.
- O regular dodecahedron→ polyhedron with pentagonal faces.
The dodecahedron is Plato's only polyhedron with pentagonal faces
It is said that Plato, who, in addition to being a mathematician, was also a philosopher, related these geometric solids with the construction of the Universe, associating the tetrahedron to fire, the cube to earth, the octahedron to air, the icosahedron to water and the dodecahedron to Cosmos. Plato believed that it was from the combination of these elements that the Universe was made.
Relationship between Plato's polyhedra and the elements that would have constituted the Universe, according to this philosopher
By Amanda Gonçalves
Graduated in Mathematics
*Mental Map by Luiz Paulo Silva
Graduated in Mathematics
Would you like to reference this text in a school or academic work? Look:
RIBEIRO, Amanda Gonçalves. "What are Plato's Polyhedra?"; Brazil School. Available in: https://brasilescola.uol.com.br/o-que-e/matematica/o-que-sao-poliedros-platao.htm. Accessed on June 28, 2021.