Hyperboloid of Two Sheets

The Hyperboloid of Two Sheets seemed like the impossible print, until I figured out the "holder" idea with the Circular Cone. The separate holder in clear emphasizes that the surface is both disconnected parts together. They find this fascinating!

The Hyperboloid of Two Sheets also works well demonstrating the relationship among it, the Circular Cone, and the Hyperboloid of One Sheet. See additional photo.

Unfortunately, the "simply printing infill" idea did not work for this holder. After several tests and variations, I designed my own shape (based on a hyperboloid of one sheet) to act as the holder. See the notes in the 3D printing settings.

Created with Mathematica and printed on my MakerGear M3-ID.

Note: Some files are rather large since I was working to get a very high resolution. I created these in Summer 2018.

See the rest of my collection. They were all designed and printed to stand at the same height, to work well for display by me during discussion in front of a classroom, and to be large enough for students to get their hands on them to really feel the shapes and the curves. We refer to these often throughout the course.

• Quadric Surfaces Set (all of the below included)
• Parabolic Cylinder
• Circular Paraboloid
• Hyperbolic Paraboloid
• Ellipsoid
• Hyperboloid of One Sheet
• Circular Cone
• Hyperboloid of Two Sheets

Approximately 193 mm tall at 100% size. The small one was printed approximately 40% scale.

I printed the "Hyperboloid of Two Sheets Half" twice. I had a difficult time getting a print I was satisfied with on both the outside and the inside. Eventually I decided on 0.2 layer height, 0% infill, 10 top solid layers, 3 bottom solid layers, 4 outline/perimeter shells, 0% infill, included a raft, and included supports to a maximum overhang angle of 50 degrees.

The "Holder" was printed with 0.2 mm layer height, 0 top layers, 0 bottom layers, 1 outline/perimeter shell, and 0% infill. No support. No raft.

I used Simplify3D for slicing.