Here is a soap-film frame for a Schwarz P minimal surface that I designed for the InforMath project funded by the National Science Foundation (DRL-1323587). The InforMath project (http://informalmathematics.org/) is a partnership between San Diego State University and several museums at the Balboa Park, including the Reuben H. Fleet Science Center (http://www.rhfleet.org/). A Schwarz P surface is a triply periodic minimal surface. The circles and lines in the frame all lie on the minimal surface. The Schwarz P minimal surface is created by soap film when the frame is dipped into soapy water.

There are several sizes for the model 6x6x6cm, 10x10x10cm and 15x15x15cm, and two choices of diameter (2.5mm and 3mm). The photos show the 10cm size 2.5mm diameter model, then the 6cm 2.5mm model.

I recommend that you send these files to Shapeways and get them printed. The frame needs to be completely supported for a successful print. (The last three photos show some of my print fails to give you a feel for the issues involved with the MakerBot 2X printer.)

On the MakerBot 2X, the 6cm model prints OK. For the larger models, I recommend the 3mm diameter model. I printed the model with supports, with a raft, and at 0.2mm resolution. The print works best when the model is solid, so 100% infill. To get the supports right, you need to do two things. First, under Print Settings, go to Custom, then Supports and Bridging. Check the support box, then uncheck the Align Supports box. Second, change the support angle from 68 degrees to 40 degrees. This will give extra sturdy supports for the entire model. The fifth and sixth photo show the MakerBot print of the 6cm size model.

On the uPrint SE printer, we printed the 10cm size 2.5mm diameter model with raft and supports, but this time we selected the button for surround under the choice of supports. A picture of these supports is shown above in the fourth photo. The first three photos show the uPrint model.

Remove the supports from the model. If necessary, you may need to use an exacto blade to tidy up the model, remove any fuzziness, and make it completely smooth.

A complete description can be found on my blog at http://mathvis.academic.wlu.edu/2016/03/02/soap-film-frame-for-the-schwarz-p-surface/

A very brief description of the mathematics can be found here: http://mathvis.academic.wlu.edu/2016/02/29/schwarz-p-surface-the-math/