Polyhedron - Definition with Examples

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Polyhedron 

A polyhedron is a 3-dimensional solid made by joining together polygons.  

The word 'polyhedron' comes from two Greek words,  poly meaning many, and hedron referring to surface.

The polyhedrons are defined by the number of faces it has. 

        Polyhedron

                                                             An example of a polyhedron 

Parts of a polyhedron

Every polyhedron has three parts: 

  • Face: the flat surfaces that make up a polyhedron are called its faces. These faces are regular polygons. 
  • Edge: the regions where the two flat surfaces meet to form a line segment are known as the edges.  
  • Vertex: It is the point of intersection of the edges of the polyhedron. A vertex is also known as the corner of a polyhedron. The plural of vertex is called vertices.

 

                                                                                                                                                 

Parts of polyhedron                

                         

The names of the polyhedrons are derived from the number of faces they have:  

Name 

No. of faces 

Tetrahedron

A polyhedron with 4 faces. 

Pentahedron

 

A polyhedron with 5 faces.

Hexahedron

 

A polyhedron with 6 faces.

Heptahedron

 

A polyhedron with 7 faces.

Octahedron

 

A polyhedron with 8 faces.

Nonahedron

 

A polyhedron with 9 faces.

Decahedron

A polyhedron with 10 faces

                  

Types of polyhedron

 types of polyhedron

                  

Regular Polyhedron 

A regular polyhedron is made up of regular polygons. Such solids are also known as ‘platonic solids’ 

 

Irregular polyhedron 

An irregular polyhedron is formed by polygons of different shapes where all the components are not the same. This means that all the sides of an irregular polyhedron are not equal. 

Some of the regular polygons are described in the table below:  

Polyhedrons in everyday life 

Examples 

Images 

Houses/Buildings: Most of the houses around us are polyhedrons as they are made of flat surfaces. 

 

example

A prism: A  prism is made of three rectangles joined together with triangular bases

Example

A football or a soccer ball


football

Pyramids: A polyhedron with four sides is a tetrahedron and is also called a pyramid.

 

                 Pyramids

 

Fun facts about a polyhedron

If we know about the number of faces and the vertex of a polyhedron, the number of edges can be calculated using the ‘polyhedron formula’ or ‘Euler’s formula’.

                                   F + V = E - 2 

where F, V, and E represents the number of faces, edges and vertices of the polyhedron respectively.

 

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