'Impossible' Pyramid Puzzle - Material Samples for 3D Printing

Need a calibration model for your desktop 3D printer, but hate having tonnes of wasted cubes lying around?

Want to test out various material samples from a 3D printing service, but don't want to pay for a swatch of useless plastic/metal/whatchamacallit cluttering up the house?

Why not make something fun with your sample material 3D prints? Any 2 units of this puzzle piece will fit together to form a tetrahedron in a seemingly impossible way! The solution is bafflingly simple yet completely unintuitive to the uninitiated.

Wear these as matching earrings, or as pendants on a chain... and always have a unique brainteaser to show off to your friends. (Yes, I'm stretching this to fit the Jewelry competition... but I also want to share this instructable with Jewelry makers out there who might like to know how easy it is to test out metal printing services.)

I designed this puzzle piece based on the old 2-piece pyramid puzzle, specifically to test out some of the materials on offer at Shapeways.com. I designed it so that it prints at the extremes of what is allowed in terms of slenderness and edge sharpness, to create a small, light and cheap print.

This is optimised to print well in all plastics, acrylics, aluminium, stainless steel and precious metals on Shapeways (or equivalent). It will not print in porcelain and sandstone as the elements are too fine.

The basic geometry of this is simple: model a regular tetrahedron and split it in two by joining the mid-points of 4 edges to form a square that bisects it.

From there I manipulate it such that each edge becomes an extruded tube. At first I modelled each edge as a triangular tube (highlighted in red), but then I found that a square tube was more printable. Also, because the faces meet at an acute angle, I had to further chamfer the edges (round them over) for printability.

Shapeways.com only accepted my model for printing after several tries, with all the above tweaks to pass all the automatic 'printability checks'.

This model is 1 inch on the longest edge, and the elements are all tubes of minimum width 1.0mm, which is the minimum allowed for most materials at Shapeways using their expensive printers. If you are using this as a calibration model for your own desktop FDM printer, you may need to scale it up 2x or more to yield a viable print.

I'm using Shapeways.com for the first time. I wanted to test a few different materials to see how they feel: weight, surface finish, durability, etc. The interface was really easy, with all the automated model checking built in to the system to make sure that what you see is what you get.

After uploading, the model page will show you the dimensions of the model, volume of material used, and most importantly whether or not the model works in each of the materials you want.

For example, this model was automatically tested by their algorithms, and should print well in all plastics, acrylics, aluminium, stainless steel and precious metals. However, it will not print in porcelain and sandstone.

The last image shows the details of why it cannot print in a certain material. In this instance the members are too small for porcelain, and the multiple openings will make it impossible to create a mold for casting porcelain without a whole bunch of separate mold pieces.

In this case, my first few attempts didn't work, and the interface highlighted the parts of the model that I needed to 'beef up' in order to get the model to pass the automated checks and be allowed for print.

So I've already done all this optimisation work for myself, so if you guys want to skip the work and just order the finished pieces, they're available directly off Shapeways.com

https://www.shapeways.com/product/9HX6CNSH4

The prices reflect the actual cost of printing, plus a small markup for my effort in modelling this and getting it just right. I'm just making it available as a convenience to others, and out of my own curiosity to see if anyone will actually buy any prints!

After ordering, just wait for the mailman to come with your parcel! These came packaged in lots of bubble wrap in a box. The samples I printed were in Stainless Steel, Bronze Steel, Metallic Plastic and Polished Metallic Plastic.

They look great, and the metal ones feel great too! The metallic plastic is as rough as it looks. That stuff is basically metal filings embedded in plastic.

Here's how to get maximum mileage out of this puzzle:

Pass it to your friends and tell them that it took the Egyptians 20 years to build the pyramids. Then challenge them to put together any 2 pieces into a complete pyramid in under 20 seconds. You could probably even make a pretty big bet, as long as they haven't done this puzzle before. It takes most people quite a while to figure it out.

Yes, I know the pyramids of Giza were square-based pyramids, while this tetrahedron is a triangle-based pyramid. That's a bit of psychological misdirection thrown into the mix to help you win the bet. ;)

Pro tip: Make them do it in their hands, instead of on a flat surface. The lack of a reference plane adds to the confusion. Better still, get 2 or more friends to race each other to find the solution first!

The secret is simple: Bring the 2 square faces together, but rotated 90 degrees to each other. Voila!

I guess the reason this is so unintuitive is that people first assume that the square sides must be at the bottom, or that the triangular faces must somehow connect to each other.

Have fun!

Oh yes, since this was a material test print... you might want to know my impressions of the materials I received.

Stainless Steel: came out yellowish, more like light bronze than steel. Some variation in colour between the yellower bits and some parts which are bare silvery steel. Very hard, with a pitted surface. Has great potential for toys, jewelry and usable tools. The steel pieces look and feel like 'vintage' monopoly play tokens, with a satisfying 'clink'.

Bronzed Steel: came out shiny chocolate brown. Same base material as 'Stainless Steel'. Pitted, very hard. Looks a bit less like 'real metal'.

Metallic Plastic: Very lightweight, does not feel like metal at all. Surface is like 120 grit sandpaper with tiny bits of aluminium powder densely packed. Edges are sharp.

Polished Metallic Plastic: Same base material, just tumbled for a bit with polishing medium. Sharp edges are smoothed down just a hair, flat faces feel smoother to touch, more like 240 grit sandpaper. I would not recommend Metallic Plastic for use in actual jewelry items or gifts. It's more for static items on display.

Here's the link to the object on Shapeways: https://www.shapeways.com/product/9HX6CNSH4

Enjoy!