Jewels of Plato Puzzle Box

Introduction

Plato was an Ancient Greek philosopher (circa. 400 BCE) whose name is associated with the five Platonic Solids - Tetrahedron, Cube, Octahedron, Dodecahedron and Isocahedron. They are more familiar today, though, as the gaming dice: d4, d6, d8, d12 and d20.

This puzzle box is inspired by Ancient Greek architecture, with Doric colums, cryptic inscriptions and is bejewelled with the 5 Solids on top. What secrets lay inside, and how to open the box to find them? (secrets not included.)

Parts

The model is made up of 18 parts, in 7 categories: Base, Lid Bottom, Lid Middle, Lid Top, Sliders, Discs and Solids. The entire box is 3D Printed, without any bolts etc.

Materials and Print Recommendations

These recommendations are meant only as a guide - all can be printed in your materials of choice! I include the materials and print parameters I ended up using - all with a standard 0.4mm nozzle. I used Creality K1 for the Base and Lid parts, and Ender 3 S1 Pro for all the others (to get an idea of slightly less-accurate print dimenstions). The tolerances are pretty tight so that the box and parts don't rattle - you may have to experiment with your particular printer (scaling on x-y and/or using x-y compensation) and perhaps sand some of the parts. Design was done with OnShape CAD and the slicer used was Orca.

• Base, Lid - Stone/Rock/Marble PLA, 0.2 mm layer height, 3x3x3 walls/top/bottom, 15% Gyroid. I was able to print without supports but the Base may need some spot Tree supports for the upper point overhangs and/or Normal support for the inner locking grooves. I also used ironing on all upper surfaces for a smooth finish.
• Sliders, Discs - PLA+, 0.2 mm layer height, 5x4x4 walls/top/nottom, 20% Grid. I only needed spot Tree supports for the outer points of the Disc with the gear, mostly for bed adhesion, no other supports. Print the Sliders upside down so that the outer edges don't have overhangs. The higher wall count is for the torque applied to the spindles of the discs. Make sure all the surfaces are flat with no little filament blobs and slivers - I ‘polish’ them with an old piece of printed PLA that has a grid pattern on it.
• Solids - Silk PLA, 0.16 mm layer height. 3x3x3 walls/top/bottom. 15% Honeycomb. Print these upside down - you may need a brim for the Isocahedron as it has a smaller contact with the bed.

Assembly

All of the exciting stuff happens in the lid, and its assembly is fairly straightforward if you follow these steps.

1. Place the Lid Bottom down on your work surface (any orientation) and drop in the 4 Slider parts. Extend the Sliders out as far as they can go - we'll be assembling the lid in the Locked position.
   
   
    
2. Clip the Lid Middle on top, and whilst ensuring that all the Sliders are fully extended, drop the Disc with the gear in the middle, oriented such that the cutout notch on the spindle is facing you. You should be able to twiddle the Gear to extend and retract the Sliders.
   
   
    
3. Drop in the other Discs such that their spindle notches are also facing you and that their triangle motifs are facing the middle. There is only one way to fit them if you follow these rules.
   
   
    
4. Clip on the Lid Top - it should only fit one way, with the ‘Boreas’ motif at the top.
   
   
    
5. FInally clip on the Solids, noting where the notches are, such that the triangle motifs on the outer Solids are facing the largest of the triangles in each placement on the Lid - this is the indicator of the fully Locked position.
   
   
    

And that's it!  To test this and make sure everything fits and works freely (see below) I initially stuck all the Lid parts together and put the Solids on the Disc spindles with Blu-Tack, a sticky putty-like material which is easy to remove afterwards. This only seems available in the UK, but similar brands I can find include Poster Putty, Mounting Putty, Prestik and Patafix.

Solution

The clues to the solution are given on the sides of the Base and on the Lid:

• Lid - Engraved on the Lid are four words, Boreas, Eurus, Notos and Zephyros. These are the ancient Greek words for the four directions, which they defined by the names of the winds. A Google search on any of them should come up with this first, with the winds being Boreas = North, Eurus = East, Notos = South and Zephyros = West. That gives us the directions we need to solve the puzzle.
• Base - On each side of the Base is an inscription, of the form Greek Letter = Number Roman Letter. The Greek letters are Alpha, Beta, Gamma and Delta, the first four letters in their alphabet, and denote the order in which to solve the puzzle. The Number refers to the number of sides each of the Solids has, similar to the Dice names mentioned above. Note that the Solids on the box have been cut in half, so the number refers the the full solid. Finally the Roman Letter is the direction the Solids need to be turned to, using the small triangles imprinted on them - North, East, South and West.

So the clues translate as follows:

• ‘alpha = 4S’ translates to: "First turn the solid that has four sides such that its triangle points towards Notos”.
• ‘beta = 20N' translates to: "Second turn the solid that has twenty sides such that its triangle points towards Boreas”.
• ‘gamma = 12W’ translates to: "Third turn the solid that has twelve sides so that its triangle points towards Zephyros”.
• ‘delta = 8E’ translates to: "Fourth turn the solid that has eight sides so that its triangle points to Eurus”.

Finally the centre Solid, the Cube, can be turned to unlock the lid!

To lock the lid, turn the Solids in reverse order such that their triangles point towards the largest of the triangles engraved beside them on the Lid.

Feedback and Remixing

This is my first Puzzle Box design, so all commentary and feedback on the model, instructions etc. is very welcome!

I'm sure that there are countless ways this mechanism can be used, re-skinning the box and introducing other shapes with their own clues as to how to open the box - I look forward to seeing what you come up with! I have included STEP files as well as STL for easier remixing - these are also better overall if your Slicer can read them directly.

Many thanks for your interest in this puzzle box!

EdinBearDragon