Ten Minimal Surface Ornaments and Spheres

These ten minimal surface ornaments and spheres can be used for decoration or just as a way of appreciating the beauty of mathematical minimal surfaces.

See here from video of printed ornaments and cross-sectional views in Cura slicing: https://youtu.be/xwHfo-ngRqM

A minimal surface can be thought of as a surface that is stretched as tightly as possible within the edges that hold it in place. The shape of a soap bubble that forms within a wire frame is an example of a minimal surface. These ornaments and spheres are derived from a special kind of minimal surface known as a “triply periodic minimal surface (TPMS),” a minimal surface that can be tiled infinitely in all three directions.

Files for each selected TPMS are provided as a “Sphere,” “Ornament,” and in some cases, as “Ornament Support.” Files are named for the type of TPMS and the mathematician credited with their discovery.

“Sphere” files are 60mm diameter spheres of each TPMS.

“Ornament” files are also 60mm diameter spheres but include pilot holes for at top for small ½ inch eye hooks. In some cases, additional geometry has been added to strengthen the area around the hook. The exception to this is the “Schoen F-RD(r)” and “Schwarz CLP” in which the geometry of the TPMS sphere already provides a means of hanging the ornament and the addition of a hook is not necessary.

“Ornament Support” files have built in supports for the upper portions of some of the more complex shapes. This allows you to reduce the amount of support you need to set up, but you will still need to set up supports for the base of the ornament. You will need to set up additional support for each file, and expect to do some post-print cleanup.

See here for more information about these and other TPMS: http://facstaff.susqu.edu/brakke/evolver/examples/periodic/periodic.html

This model is submitted to the November 2021 "DIY: Don't Buy 3D Modeling Challenge" in the "Holiday DIY" category.

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