I did a test with cardboard, planning to migrate to balsa wood, but after the project was completed, I liked the result so much that I kept it as it was.
Tinted transparent paper
Table Saw or Router
Corel Draw (R) or any other vector-capable software
Danish oil (or any other wood stain/finish)
Step 1: Preparing the Project
For your convenience, and out of my generosity, i made the Corel draw file available HERE.
Just open and you should be good to go. Just a comment: there are other decorations in the file, they are hidden and print disabled (see the layer named "non select").
Follow the guidelines for the power and speed depending on the cardboard thickness.
Since the design is very complex, I suggest to either increase 10% the power or decrease 10% the speed, because you don't want to end up with parts not completely cut through, and need either to redo the job or -even worse- to cut the pieces manually with a knife!
Step 2: Cutting
You will notice that one side has the typical "laser burns": don't worry, we'll take care of this the next steps.
Step 3: Finishing the Exterior Side
Lay the pieces on a mat or cardboard, with the side with "Laser burns" down.
With a steady flow, spray several coats of poly, letting it dry within coats.
The poly will dry fast, because the cardboard will absorb it. Be careful not to insist too long on a spot, or you will wet the cardboard and make it look darker.
Step 4: Cover the Inner Side With the Paper
Cut 4 squares of the transparent paper so that it covers the openings and does not interferes with the junctions.
I suggest you use a stick glue, paying attention not to have any glue bleed through the openings in the design.
Once finished, let the glue dry while we will take care of the lamp's base.
Step 5: The Base
Measure the inner dimensions of the panels (inside the grooves): this will be your template for the grooves in the plaque. If you used my design, this dimension will be 5in.
The idea is to cut a square pattern of grooves in the plaque where the 4 panels will fit in.
You can do this with a table saw or a router.
I used a table saw and just make sure you set the height of the blade to 1/4 in.
Center the design so that the 5x5 in. square will be equally distant from the sides.
Set the guide of the table saw at 5 and 7/8 in. and run a first pass on all 4 sides.
Check the clearance and adjust the giude so that you will be at 6 in and do another pass.
Make sure that the panels can fit inside the grooves you just cut or adjust accordingly.
Once done, fit the panels together and insert them on the grooves, pay attention to the paper on the inside.
If everything looks great, you now can finish the base with your favorite stain and finish (I used Danish oil, for a natural wood finish)
Step 6: Final Step
If you are concerned about the lamp getting hot, you may want to cut some openings on the base of the panels, and I suggest to do it on the initial design, but then you will have to cut through the transparent paper with a knife, but the look will be much better.
If you don't want to do it on the design, just use the paper hole puncher used to cut holes on documents, just make sure the cut comes out clean or you will ruin the panel.
You might also want to fix the candle to the base either by having a nail coming through or pouring few hot wax drops to keep the candle in place.
DO NOT LEAVE THE LAMP UNATTENDED!