Stiffened Polygons

Polygons with 3d-printed strands as mechanical reinforcements.

To introduce stiffness to a polygonal frame multiple triangles are inscribed into the shape, changing rotation with z-height. The triangles themselves are strands of filament extruded into the air. This technique is called bridging, because it doesn't make use of support structures (eventually the different triangles may touch each other). Each strand consist of two layers.

The diameter of all three polygons - pentagon, hexagon and heptagon - is approximately 10cm. The rotation of the triangle is bound to 1/3 of the length of the polygon outline, not to an angle. Therefore this principle is adaptive to the applied shape and every curve point is connected to exactly two strands. The result has a relative high stiffness compared to the amount of material used.

Geometry was created using Rhino/Grasshopper.

Print Settings


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The examples were printed using the default "0.2mm Quality" from PrusaSlicer on a Prusa i3 MK3S. Extrusion width was 0.45mm, "Thin Walls" option should not be necessary.

Stereographic Projection

This model is featured in figure 3.12 of Visualizing Mathematics with 3D Printing.

Stereographic projection is a map from the sphere to the plane: Imagine straight lines going from the north pole of the sphere down onto the plane. Each line hits the sphere in one point and the plane in one point. Stereographic projection maps that point on the sphere to the point on the plane.
If you put a light source at the north pole of this sculpture, the rays of light effectively do stereographic projection! The curves on the sphere cast shadows, mapping them to a straight line grid on the plane.
Stereographic projection is also available at Shapeways.

Update: added a version of the file with a wider base for easier printing.

A Fully Printable Microscope

Well almost, you still need to locate 4 lenses from some disposable cameras and a light source.

For the light source use an LED or mirror, whatever you have. I used a cheap LED wall light from Wal-Mart.

For the lenses, I went to a local photography shop and they were very kind to give me an entire bag full (Thank you Lens and Shutter! Since I had so many, I designed it to work with them all. There is a different optical tube that you have to print for the Fujifilm lenses (11.9mm outer diameter) vs. the Kodak lenses (13.2mm outer diameter). It should work with the following as I measured them all and will likely work with others as well:

(CAUTION there is a significant shock hazard if you plan to open a flash camera from the capacitor!)

Fujifilm QuickSnap Outdoor
Fujifilm QuickSnap Flash
Fujifilm Flash

Kodak FunSaver Flash
Kodak unaned
Kodak Max Outdoor

The magnification of this microscope is expected be near 74x (still need to confirm precisely).

Focus Lock: :
Smartphone Adapter:

This project was also inspired by this excellent project:
and this:


This should work with a variety of printers and settings. I printed it on a Makerbot Rep 2 using black, silver, and white PLA. For the optical tube, rack, knobs, pinion, stage, and head I used 0.1mm, 15% fill and high setting. For the post and stand I used medium settings, 0.27mm, 2.5% fill. It should have enough tolerance for medium settings everywhere.

Looking forward to your feedback on the build.