Platonic Solids: Why only five of them?
Regular polygons are polygons with congruent sides and congruent interior angles. In three dimensions, the equivalent of regular polygons are regular polyhedra — solids whose faces are congruent regular polygons. The most common regular polyhedron is the cube whose faces are congruent squares. The other regular polyhedra are shown below.
Regular polyhedra are also known as Platonic solids — named after the Greek philosopher and mathematician Plato. The Greeks studied Platonic solids extensively, and they even associated them with the four classic elements: cube for earth, octahedron for air, icosahedron for water, and tetrahedron for fire. » Read more