ALL ABOUT POLYHEDRONS

POLYHERDRONS

A polyhedron is a solid with flat faces (from Greek poly- meaning "many" and -hedron meaning "face").

Each face is a polygon (a flat shape with straight sides).

So no curved surfaces: cones, spheres and cylinders are not polyhedrons.

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

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.

Is a cube a polyhedron?

In geometry, a cube is a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex. The cube is the only regular hexahedron and is one of the five Platonic solids. ... The cube is the only convex polyhedron whose faces are all squares.

Only five regular polyhedrons exist: the tetrahedron (four triangular faces), the cube (six square faces), the octahedron (eight triangular faces—think of two pyramids placed bottom to bottom), the dodecahedron (12 pentagonal faces), and the icosahedron (20 triangular faces).

So, Polyhedrons are classified and named according to the number and type of faces.

A polyhedron with four sides is a tetrahedron, but is also called a pyramid. The six-sided cube is also called a hexahedron.

A polyhedron with six rectangles as sides also has many names—a rectangular parallelepided, rectangular prism, or box.

ICOSAHEDRON

In geometry, an icosahedron is a polyhedron with 20 faces.

Number of faces: 20

Number of vertices: 12

Number of edges: 30

Volume: 5×(3+√5)/12 × a³

Side shape: Triangle

DODECAHEDRON

Net of dodecahedron

A regular dodecahedron or pentagonal dodecahedron is a dodecahedron that is regular, which is composed of twelve regular pentagonal faces, three meeting at each vertex. It is one of the five Platonic solids. It has 12 faces, 20 vertices, 30 edges, and 160 diagonals (60 face diagonals, 100 space diagonals).