Platonic solids are five. They are the essential basis for all other solid Geometry. The 5 platonic solids are polyhedra with regular polygon faces. The faces and vertices are identical. They are referred as perfectly symmetrical polyhedra. Each platonic solid obeys their relationship # of faces+ # of vertices= # of edges+2(Euler).If a solid has to be a platonic solid, the figure must use the same regular polygon for all its faces and have the same number of faces meet at each of its vertices.
The platonic solids and their regularities were originally discovered by Pythagoreans and they were called the Pythagorean solids. They were later named by the Greek Philosopher Plato who wrote about them in detail in his book ‘Timaeus’.
The Tetrahedron
The Tetrahedron is bounded by four equilateral triangles. The number of vertices is three. The number of polygons meeting at a vertex is three. The number of faces for tetrahedron is four. The number of edges of the tetrahedron is six. The number of vertices of the tetrahedron is four.
The Hexahedron
The hexahedron is a platonic solid. It is bounded by 6 squares. The number of vertices is four. The number of polygons meeting at vertex is three. The number of faces is six. The number of edges of the hexahedron is twelve. The number of vertices for hexahedron is eight.
The Octahedron
Octahedron is a platonic solid. It is bounded by eight equilateral triangles. The number of vertices is three. The number of edges is twelve. The number of polygons meeting at a vertex is four. The number of faces for an octahedron is eight. The number of vertices of the octahedron is six.
The Dodecahedron
The dodecahedron is a platonic solid. It is bounded by twelve equilateral pentagons. The number of vertices is five. The number of polygons meeting at a vertex is three. The number of edges of a dodecahedron is thirty. The number of vertices is twenty. The number of faces is twelve.
The Icosahedron
The Icosahedron is a platonic solid. It is bounded by twenty equilateral triangles. The number of vertices is three. The number of polygons meeting at a vertex is five. The number of faces is twenty. The number of edges of the icosahedron is thirty. The number of vertices is twelve.
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