Dodecahedron Jewelry Design

In order to get a three dimensional hexagon-based design I knew I wanted a 4-axis environment instead of a normal 3-axis environment because a dodecahedron does not have 90° based geometry but 120° based geometry. So in order to get those axes I created a regular tetrahedron using SolidWorks equation function. I created 4 axes, one normal to each face of the pyramid. I then sketched a hexagon with a globally defined size to slice through the solid along each new axis. This produced the rhombic dodecahedron shape. Unfortnately SoldiWorks equation function rounds to two decimal points so I did some rounding error correction to even out the dodecahedron.

In order to take this from an appealing geometric shape to an appealing piece of jewelry I designed it for manufacturing using 3D printing. I copied the body and made two smaller versions of it: one to file away the sharp edges on the outside and one to hollow out the inside. From there I created an offset pattern on each face and lofted it to create an inverse stellation. Because of the nature of the shape of a dodecahedron, creating a 12-instance pattern could not be done linearly or circularly. I attempted to create a loft pattern with SolidWorks table driven patterns but the process was too brittle. Instead I created the lofts individually but I linked them together by driving them entirely with global variables so that way if I wanted to change the nature of the loft I could do so in one step. For the plastic design I hollowed it out with some thru holes in the smaller rhombuses. These 3mm holes are adequate to clear the model of any residual powder. The metal design needs larger holes and an internal cavity. For both designs I used one of the smaller bodies I created earlier to remove the sharp external corners. I could have just used a fillet without doing the truncation but the truncation allowed me to size the overall dimensions with more specificity based on the scaling of the smaller body.

With the basic design achieved, I put a ring on it and smoothed out the design to turn this shape into an earring. I made sure that the ring was 1.3-1.6cm thick (depending on the material) so that it would be adequate to hold the weight. For the metal design, I used the smaller of the two bodies I duplicated earlier to hollow out the internals which I then smoothed. Initially I tried shelling the design but, while this created the uniform thickness which is ideal for 3D printing, it created too much volume in areas that didn't need it and left sharp internal features. This would have made it larger, heavier, and more difficult to plate and polish. For 3D printing in plastic, having small sharp internal features are acceptable and even desirable. But small openings and sharp edges would lead to very uneven finishes on the internal surfaces of the metal part.

Once I had an overall design I was happy with then it was on to smaller refinements to the DFM (design for manufacture).

I created two versions of the model: one 3D design for plastic & one 3D design for metal. When designing for manufacture each process has different considerations (machining vs molding vs printing etc). Each specific material also has different DFM considerations. First and most obvious, metal is much more expensive and heavy than plastic so I need to minimize the volume. I ensured that the total material volume remains around 0.7cm³ for two reasons: weight and cost. I knew what price point I wanted the metal earrings to be at and since the cost of metal 3D printing is largely dependent on volume I knew what number I had to stay under. By comparison, plastic is cheap enough that material volume is not a driving consideration.

When designing anything you have to consider the worst case usage scenario. For earrings, that means someone who'll be wearing them on a long active day which means they'll be bouncing around into their face and hair and possibly getting snagged. I designed the openings of the earring to be small and inset to avoid snags but large enough for DFM considerations (plating and polishing). As far as weight goes 5-7 grams is about as heavy as you should design an earring for comfortable all day use (although each person's comfort level is different). For the metal design, since I ensured that the finished piece would have a total volume of 0.7cm³ that means that in plated brass or steel each earring would weigh 6 grams. For plastic, the volume is 3.7cm³ and the weight is 5 grams. Large metal earrings feel more cumbersome than large plastic earrings so I also reduced the size for the metals earrings. The plastic earrings are 2.4cm wide and the metal earrings are 1.6cm wide (33% smaller). That way if the earring bounces into your face, the smaller and more rounded it is the better.

Metals will be hand polished so I designed it with very large radii so that the edges will all be uniform. I don't want to take the chance the some edges will break during secondary processing and the final product will have some edges rounder than others. What a shame it would be to go through the trouble of making a uniform geometric figure and have it end up lopsided! Because of the multistep nature of printing in metal, fragile parts can break easily so I designed each edge to be thick enough to support the weight of the whole body.

Because of the nature of the small openings on the design there's no way to hand polish the internal surfaces. I don't really consider this a problem as I like the contrasting look. However part of the reason that the holes are larger on the metal design is to ensure that the surface plating will be even. Having some spots rougher than other's isn't so bad but if there were areas that were not able to be plated and it left bare steel patches where there should be gold/rhodium then that would not only look terrible it would make it more prone to rusting.

Personally I like the plastic design more as it's more true to my vision. When designing for metal I had to make some compromises. The internal structure is more hollow than I would like but it's necessary. It looks more like connected wires that a sculpted solid part but in order to get the latter look I would have had to have made the overall size much much smaller. Maybe once I'm wearing them for awhile I'll decide that's the next sensible iteration but at this point I like them how they are.

You could make the argument that most of these steps are unnecessary work and over-engineering. It's just jewelry! Who cares! It's not like it's a housing for an autonomous undersea vehicle. (Okay, yes, maybe the industrial engineering I do has me predisposed to think through every failure possibility even when it isn't critical.) But if I didn't design it robustly then it might not be able to be reliably 3D printed and polished successfully every time if the 3D printing company changes their processes or standards. And even if it does look good on the first day, jewelery is something people own and wear for a long time that goes through a lot of abuse. I want to ensure that everything I make can be enjoyed for as long as possible.

These earrings can be purchased from Shapeways through my shop.

The 3D files can be downloaded here:

  • Metal STL
  • Metal SolidWorks
  • Plastic STL
  • Plastic SolidWorks
  • Please contact me to request access to download the files.

    I've uploaded images which show a step-by-step walkthrough of my SolidWorks design process.

    I designed the model geometrically rather than sculpturally because, as an engineer, that's how I think about design.

    I really like the hexagon both as a shape and because it's the most popular shape in euro boardgames, so I went into the design knowing that I wanted some sort of a 3D version of a hexagon. Because of the hexagon's angular nature I knew I couldn't create the shape I was looking for with the standard 3 axes 90° offset from one another so the design took off from there.

    Because this is a personal project I can talk about it more in-depth than I can my corporate projects.