Polyhedron definition states that “a threedimensional structure in Euclidean geometry, made up of a finite number of polygonal faces”.
The boundary between the interior and the exterior of a solid is a polyhedron.
Polyhedrons, in general, are named according to the number of faces.
Parts of Polyhedron
The Polyhedron has three parts namely:
The face is a flat surface that makes up a polyhedron which is regular polygons.
Edge is the region where the two flat surfaces meet to form a line segment.
Vertex, also known as a corner, is a point of intersection of the edges of the polyhedron.
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Types of Polyhedron
There are three main types of Polyhedron:

Prisms
A prism is a polyhedron consisting of an nsided polygonal base, a second base that is a translated copy of the first, and no other faces that connect the two bases to corresponding sides.
Prisms are named according to their crosssections(polyhedron faces).
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Platonic Solids
A regular, convex polyhedron is a Platonic solid in threedimensional space. It is constructed of congruent, regular, polygonal faces that meet at each vertex with the same number of faces.
Platonic solids are of five types based on Polyhedron faces and polyhedron shapes:

Tetrahedron

It has 4 faces, 4 Vertices, and 6 Edges.

It has 3 triangles that meet at each vertex.

The surface area of tetrahedron= [sqrt{3} a^{2}]

The volume of tetrahedron= [frac{sqrt{2}}{12} a^{3}]
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Cube

It has 6 faces, 8 Vertices, 12 Edges.

It has three squares that meet at each vertex.

The surface area of the cube= 6a2

The volume of the cube = a3
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Octahedron

It has 8 faces, 6 Vertices, 12 Edges.

It has 4 triangles that meet at each vertex.

The surface area of Octahedron = [2 sqrt{3} a^{2}]

The volume of Octahedron = [frac{sqrt{2}}{3} a^{3}]
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Dodecahedron

It has 12 faces, 20 Vertices, 30 Edges.

It has 3 pentagons that meet at each vertex.

The surface area of Dodecahedron= [3 sqrt{25 + 10sqrt{5}} a^{2}]

The volume of Dodecahedron = [frac{15 + 7sqrt{5}}{4} a^{3}]
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Icosahedron

It has 20 faces, 12 Vertices, 30 Edges.

It has 5 triangles that meet at each vertex.

The surface area of Icosahedron = [5 sqrt{3} a^{2}]

The volume of Icosahedron = [frac{5(3 + sqrt{5})}{12} a^{3}]
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Pyramids
A pyramid is a polyhedron created by connecting a polygonal base and a point, called the apex. A triangle, called a lateral face, is formed by any base edge and apex. It is a conical solid with a foundation of polygons.
The types of pyramids are named after the base of a pyramid.
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Counting Polyhedron Faces, Edges, and Vertices
Euler’s formula relates the number of faces, vertices, and edges of any polyhedron. This formula is used in Counting Polyhedron Faces, Edges, and Vertices.
Euler’s formula is given as follows:
F + V – E = 2
Where F = Number of Faces
V = Number of Vertices
E = Number of Edges
Problems on Polyhedron Faces, Edges, and Vertices
1) The Polyhedron has 6 faces and 12 edges. Find the number of Vertices. Also, name the type of Polyhedron.
Ans: Here to find the number of vertices we will use Euler’s formula,
F+ V – E = 2
From the question F = 6, E = 12, V = ?. Substituting these values in the Euler’s formula we get,
6 + V – 12 = 2
V – 6 = 2
V = 8
Here we can conclude that the Polyhedron is a Cube.
2) The Polyhedron has 5 faces and 6 vertices. Find the number of edges. Also, name the type of Polyhedron.
Ans: Here we will use Euler’s formula to find the number of edges,
F + V – E = 2
From the given data F = 5, V = 6, E = ?. Substituting these values in the Euler’s formula we get,
5 + 6 – E = 2
11 – E = 2
E = 9
Therefore the polyhedron is a Triangular Prism.
Fun Facts

The word Polyhedron comes from the Greek words “poly” meaning many, and “hedron,” meaning surface.

Polyhedron means that to form a 3dimensional shape, numerous flat surfaces are connected.
 < p role="presentation">Polyhedra is the plural of a polyhedron.