Faces, Edges and Vertices

Faces: The polygonal region of any solid is called its faces.

Edges: The line segments along which two faces intersect

Vertices: The points at which three or more faces meet.

Polyhedron

A three dimensional shape whose faces are polygon is known as polyhedron. It is derived from greek word 'poly' means "many" "hedron" means "face". So polyhedron is a three dimensional object with many faces.

Example
The faces of cube are squares. The faces of rectangular prism are rectangles.

Polyhedrons:

Triangular Prism             Cuboid                   Octahedron

Not polyhedrons : Those solids which have curved surfaces are not polyhedrons.

Convex polyhedrons :
If the line segment joing any two points on the surface (includes faces, vertices and edges) of the polyhedron lies on the surface and does not intersect itself is called a Convex polyhedron.

CONVEX POLYHEDRA

We know that a polygon is called a non convex polygon if the line segment joining any two vertices does not lie on the polygon. Similarly we can define for polyhedron. Given below are few examples for non convex polyhedron.

Regular convex polyhedron

The solids which are convex and whose faces, edges and angles are congruent are called regular convex polygons.

Examples of solids which are regular convex polyhedron are tetrahedron, cube, octahedron, dodecahedron and icosahedron.

Regular Octahedron : On Octagon with eight equilateral triangles as faces.

Few more examples of regular convex polyhedra are given below.