Platonic solids are regular convex polyhedrons. These polyhedrons have equivalent faces composed of regular congruent faces. The same number of faces meet at each vertex. There are 5 types of Platonic solids- Dodecahedron, Icosahedron, Octahedron, Tetrahedron and the Hexahedron.

Plato, an Athenian philosopher used the existing concept of the platonic solids to connect his world to the real world. He represented the 5 platonic solids as 5 different elements and the dodecahedron as the heavens; The hexahedron as earth, tetrahedron as fire, octahedron as air and icosahedron as water. 

These are the initial sketches of how the solid would come together:

Below, I have shown the process of how I developed a lamp using all the 5 Platonic solids which have been fit into one another.

This prototype was made with the soldering rod used by fabricators. The sizes for each solid were cut and each solid was made separately. In the end, all of the solids were put into one another and welded.

The dodecahedron was made in two separate parts as it was the last solid which would complete the entire structure.

This is how it finally looked after I had spray painted it:

This first model was made by working from inwards to outwards, which started from the icosahedron and ended with the dodecahedron.

There are a lot of issues with the this prototype. all the rods aren't perfect and the entire structure is not stable. One of the main features of this design is that all the vertices touch the consequent solid, but unfortunately, the innermost solid, the icosahedron's vertices do not touch all the sides of the octahedron. 

PROTOTYPE TWO:

For this prototype, wrought iron was used and the entire process started from the outside. So the dodecahedron was made first and the icosahedron was made in the end. 

This is how the final structure looks like: