# Three Intersecting Cylinders

My latest project was to create three intersecting cylinders and the area of their intersection. I created these objects similarly to the two intersecting cylinders and the Steinmetz solid. For the volume common to all three cylinders I used a Mathematica code and imported the object into Cinema 4D.

For the three cylinders I created them from scratch in Cinema 4D using the ‘Tube’ object. Creating the three cylinders was very straightforward. After my fail from the two cylinder object I also wanted to create the three intersecting cylinders cut in half, so the inside was visible. This proved to be a little more complicated. I used a ‘Cube’ and ‘Boole’ with each tube in order to get half cylinders. Then I was able to merge them together using a very similar process to putting equations on solids in Cinema 4D.

I have yet to print the half cylinder object, but I did print the inside intersection. The first time I printed it I ran into a problem that also occurred with the Steinmetz object. Both solids seemed to have ‘melty’ sides. The angle of the object was such that no supports were needed and yet gravity seemed to affect the plastic and cause some issues. We think that the plastic filament cooled and shrunk during printing causing the deformations.

In order to fix this I decided to reprint the inside intersection with a different orientation. this required more supports but we had much less melting on the sides. I plan to try reprinting the Steinmetz object with another orientation to see if I can eliminate the deformed sides.

The original orientation is on the left and the new orientation is on the right. The objects can be found on Thingiverse here and here.

# Intersecting Cylinders – The Steinmetz Solid

My next goal was to print two cylinders whose axes intersect at right angles and the volume common to both, otherwise known as the Steinmetz solid. I began by modeling these objects in Mathematica so I could import the objects to Cinema 4D as well as create an interactive Mathematica worksheet about these objects.

Here are the Mathematica representations of two objects I planned to print:

I exported the top object as a .wrl file into Cinema 4D since it was already a solid.

For the bottom object,  I decided it would easiest to create it from scratch in Cinema 4D using the “Tube” object and simply adjusting the dimensions and orientation.

I attempted to print the intersecting cylinders on the Afinia printer in the Math Department. It failed to finish printing because the filament got tangled coming off of the spool. However this was not a complete fail since it shows the inside of the two cylinders and can still be used as a teaching tool.

I am currently attempting to reprint it and will see how it goes!

Update: The filament got tangled once again while I was printing resulting in a similar object to the one above. We decided that these were both better teaching tools than the original design and decided not to try to print again.

I printed the Steinmetz solid on the MakerBot 2x and had great results! This object can be found on Thingiverse here and here.