PENROSE (IMPOSSIBLE TRIANGLE)

Here is my interpretation of the Penrose triangle. 

This project started as a 3am curiosity, I was not sure if the geometry could convert to anything meaningful in 3 dimensions, but many many iterations later, I was able to figure out the optimal 3D geometry for the Penrose triangle (in my opinion), and only later realizing this was already attempted by other artists and designers on makerword and elsewhere, even so, I believe I was able to arrive at a more geometrically accurate version of any 3D Penrose triangles I've come to find online (I can explain), so I figured it was still worth uploading for others to enjoy.

I have uploaded a generic version, a version with a wall mount, and one with a through hole for hanging with strings, or to wear as a pendant necklace/earing. (Not visible in 3D viewer as they are added as modifiers to the original design).

The model can also be scaled for various uses. If you need any additional sizes, or run into any problems with the mounting point/hole becoming too large or small as you scale, feel free to let me know and I will send you an updated model.

Print: 

For this design, I wanted to keep the geometry as natural and accurate as possible without any added facets…etc, so that it can be viewed in its most natural form from all angles. Due to the resulting 3D geometry however, I find that its best printed in 2 parts then glued together. This greatly enhances the final print quality on all sides and increases printing speed. 

Assembly:

Simply add a 3-4 drops of superglue, rub each end together to cover the entire surface area on both ends (avoid adding too much superglue to avoid spill over onto the visible exterior surfaces). Use acetone to remove any visible superglue remnants. If you are using a textured plate, you can also sand both ends until the textured pattern is no longer visible. This ensures a flush contact between both surfaces and the final part should look absolutely seamless.

You can also use a small amount of 3D printing resin, then lightly clamp the 2 parts together, and allow the part to cure under UV light. 

Info:

For anyone still reading this, the main deciding factor in the final geometry and shape of the 3D Penrose triangle (as compared to other models online) is choosing the slant line for side B (shown in the image below). Choosing either the green or red solid lines while keeping the dashed green line flat, results in a sudden change in elevation at the green or red lines, resulting in a visible fold line and otherwise, a relatively flat model. More realistically however, side B would begin its decline at point X (along the slanted outer edge of the triangle), and gradually decline to meet the bottom edge of the adjacent side in a linear manner, this would lower the connection point between the dashed green edge, and dashed yellow edge, requiring the dashed green line to also slant, and thereby lowering the connection point at the end of the green line and dashed cyan line, which in turn would require the dashed cyan line to also slant and so on, creating a more natural and seamless transition between sides A and B.