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A polyhedron is a 3-dimensional closed figure made from flat sides, or 'faces'. There are an infinite number of them. A barn, for example, has many flat surfaces or faces; it's a polyhedron. So it a textbook. A prism. The diamond in a ring. All these figures are made from flat 'faces'. But on eacc one of the objects mentioned above , some of the faces are different shapes. Is there a polyhedron with all the faces the same? Yes there is. In fact, there are just five of them! You are familiar with at least one of them ... the cube! It is a polyhedron with 6 faces all the same (they're all squares). Figures with all sides the same are called 'regular', so a cube is a regular 6-sided polyhedron. 
As mentioned above, there are only five polyhedra with sides that are all the same. If the sides are squares, you can make a hexahedron (cube). If you use equilateral triangles instead, you can make three other 'regular' polyhedra ... the tetrahedron (4 equal faces), the octahedron (8 equal faces), and the icosahedron (20 equal faces). 
There is also a polyhedron made from regular pentagons. It has 12 faces, all regular pentagons, and it's called a regular dodecahedron. 
These are the only regular polyhedra that exist! No other 3-dimensional object with flat surfaces can exist and be made from surfaces that are all the same. For a closer look at each of the five regular polyhedra, we have a special page where you can see a 3-D model of each figure, and rotate each in space to see it from all sides. You get two views, one as a wire-frame model that you can see through, and if you select 'FILL', a solid model. |