This instructable includes:
1. How to design these shapes in Blender.
2. A little bit of generative art making process.
3. How to turn a 3D model into a flat paper form.
4. Having the flat paper form laser cut.
5. Assembling the paper form.
6. Finishing paper to be fire resistant.
Step 1: Cylinder 1
Make a new blender project, and clear the starter cube.
Make a cylinder with closed ends. On the left side adjust it to have from 5-9 sides (I made one with each.) Make it 1.5 in radius and between 3 and 5 tall.
With the cylinder highlighted, switch to edit mode.
Select the top face. Subdivide it. Choose a number of cuts between 1 and 3 (you can go higher, but you'll have to assemble it so fewer is better for that.) Turn on "quad/tri mode."
This is the generative part of the project - set a number in the "fractal" box - I set all of mine at 5. This will randomly break this surface into a shape that you have no control over.
Go to Mesh>Faces>Triangluate Faces to turn that top into a fractured collection of pieces.
Now we have to slightly modify our randomly created form because ours will exist in the real world and it needs to follow the rules of physics. Deselect all of it and switch to selecting vertices. Rotate around the form. Anywhere that a plane passes through another plane you'll need to change it. The easiest way to do this is to select a point and drag it around until the plane cross issue is resolved. Be sure to leave the bottom of the cylinder alone - it needs to be flat to the earth so that it will be balanced when there's fire over it later.
Keep working your way around the shape until no crosses or overlaps remain. Then adjust it for aesthetics as you see fit.
Step 2: Cylinder 2
Make a new cylinder, this time with 16 faces, a diameter of .4375 and a height of 1 (for standard taper candles.)
You'll need to align this cylinder so it's centered on the top of the other cylinder. I use the global location to do this, but you could also do it by eye. Drop it down into the top of the cylinder so it's just barely showing through the top.
Then select the first cylinder, and the wrench (object modifiers) icon in the lower panel of the screen. Add the "boolean" and set it to "difference." Then select Cylinder.001 to the right. Apply it, then delete the small cylinder. You should have a nice neat candle holder drilled into the top of you faceted cylinder.
Step 3: Flattening the 3D Model
Another alternative is the Import-Export Paper Model Add-On created by Addam Dominec. I used this because it was better for my particular application. Install the Add-On and you can use it to export your model as a .svg. It includes tabs for gluing and mountain/valley fold line indications.
Step 4: Making the Model Laser Ready
Open it in a .svg and vector friendly program (Inkscape, Illustrator, etc.)
Your laser requirements will vary (if you're using a service they'll explain them, if you're using a hackerspace you probably took an intro course that told you what you need to know.)
Make sure the model is the right size - the circle at the bottom of the candle spot should be .875 inches. If it's not, adjust the size of everything equally until it is .875.
I created one path for the outside cutting edge and another for the score lines. You can only score on one side which isn't perfect for paper craft but it is for lasers. The scores on the wrong side are just guidelines for those creases.
Also arrange your parts to fit the cutting bed of the laser. You may have to cut some things apart to do it, just be sure to add tabs so you can re-assemble them later.
Of course, if you don't have laser access you can just print off the pattern and use it that way instead!
Step 5: Preparing the Paper
I wanted an oxblood red color. I layered washes of acrylic paint onto the paper, mostly in alizarin crimson, but with some antique copper to keep the color warm and some dioxazine purple to vary the red tones a bit. Keep adding layers of glaze until you reach a color you like - the color when wet is most important, as the finishing steps will give it a permanently wet look.
Step 6: Laser Cutting/Marking
Mark the mountain folds so you know which they are (I used small x's.)
Pre-crease your models. Do a bit of dry assembly to make sure you know where everything is. Refer to the 3D model in blender if it helps.
Step 7: Assembly
Assemble the actually candle holding pieces first. Glue them into place, and then add an extra layer of glue over the tabs on the back of the paper to keep them super secure.
Continue carefully assembling the model until it's completely glued and dried. Add layers of glue on the inside wherever you are concerned about the strength.
Touch up the paint if you need to.
Step 8: Finishing Coat
Resin is crazy dangerous stuff. You need gloves, long sleeves, safety glasses, and anything else you can come up with to protect yourself. You'll also want waxed paper and newspaper for your work surface. Read everything that comes with your resin so you know all the safety info.
Set up a place to set them to dry (technically harden.) I set them on pennies but that was really just a good way to glue pennies to them. Either set them on something high (like a small overturned paper cup) or right onto the waxed paper and let the extra resin pool around the bottom.
I used a small marked cup and popsicle stick for mixing the resin, and a disposable brush to apply it to the surface of the pieces. Mix up the resin as per manufacturer instructions (I added a touch of red resin dye for extra color depth.)
Hold the model securely near the bottom with a gloved hand.
Carefully brush a coat of resin over everything but the bottom, paying extra attention to sealing where the candle will actually sit.
Set the model down and brush in where your fingers were.
Breath on any surface bubbles - CO2 helps to pop them.
Leave the models for at least 24 hours.
Step 9: Use Them
Of course this is still paper and fire, you are accepting the risk of fire by using them. Pay attention to them, set them somewhere far from other combustible materials, and realize that they could burn down (especially if there's a gap in the resin. I wrapped a bit of tinfoil around the bottom of each candle for safety, and I set them on a metal tray. I like the element of living a little dangerously. I also sort of like the idea that something I put so much work into could spontaneously burst into flames. The candles shown were quite disappointingly were non-drip, though I specifically looked for candles without that on the label. My concept included the idea of wax puddling up on them as they were used, so I'll be candle shopping again until I find the right kind.
These could easily be modified to vases or some other form (no fire risk then, either), once you know the process it's all about designing what you want to make.