Hyperbolic Cube

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Annnyway…

This model is a geometrically accurate 3D representation of a hyperbolic cube.

I created it while experimenting in CAD, exploring hyperbolic geometry. It represents a cube in hyperbolic space with negative curvature on all six faces.

Important Note: FDM printing has its limitations with this shape due to the nature of hyperbolic geometry. The sharp points likely won’t come out perfectly, but you can improve the results by tweaking print speeds toward the end and experimenting with different orientations. (I’ve included 3MF files for a couple of orientations I’ve tested.)

If needed, I usually snip the tips slightly for a cleaner look—just a small clip, and you’re good to go! The tips are delicate, so handle them with care. Though it can be a challenge, this shape is absolutely worth printing.

I have no idea how it would perform with resin printing, but I’d love to see the results if you give it a try!

I’ve included some 3MF files for printing the model in two halves. To capture the full form of the Hyperbolic Cube, print both halves and glue them together. Masking the seam where the parts join is up to you. Some people use paper clay, wood filler, and paint for a seamless finish.

Alternatively, you can print just one half, which offers a unique perspective on its own and makes a great base for displaying a spherical object.

In certain orientations, slicing may generate an undesirable pattern on the center of the curved faces. This pattern resembles a target-like formation of concentric rings (see photos).

You could try using variable layer height to make the pattern less noticeable, though I haven’t tested this myself, so I can’t say for sure if it will help. Alternatively, you can avoid this issue entirely by printing the model in halves using the diagonal orientation, as shown in the photos below.

If you prefer printing in a different orientation and plan to finish the model, you can fill in the pattern using wood filler or paper clay, and then paint it for a smooth surface.

Print Settings:

(Here are the settings I've been using, but I'm interested to hear your thoughts on any settings that you think would work well with these hyperbolic shapes.)

Supports: None
Infill: Gyroid, 10% (adjust to preference)
Brim: Not required, but use one if you're having adhesion issues
Top Surface Pattern: Archimedean Chords (this setting is irrelevant if printing in the diagonal orientation)

Feel free to leave a comment or reach out if you have any questions. I’m here to help.

Have fun! 🥳 

License Information:

This model is licensed under Creative Commons Attribution-NonCommercial-ShareAlike (CC BY-NC-SA). You may share, copy, and redistribute the file for non-commercial purposes with proper attribution. Modifications must remain under the same license. Selling this model or modified versions, either digitally or as physical prints, is strictly prohibited.

*Selling physical prints of my designs is only permitted if you are an active member of my Authorized Seller tier on Patreon, Printables, or MakerWorld.* To learn more, visit https://www.patreon.com/c/endlessdesignlab

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