These are Triply Periodic Minimal Surface Structures, or TPMS for short. These structures have mesmerising and complex shapes with a great history in mathematics in the shapes of soap films. Check out this documentary for more information.
Essentially, wireframes and soap bubbles can be used to generate 'minimal surfaces'. If you've ever blown bubbles before, you know the shapes detergent films can make across wireframes. If you use a variety of wireframe shapes, you can generate 'minimal surfaces' as they will always make a shape of the smallest surface area possible to stop from bursting. Mathematicians studied these shapes and were able to quantify the 3D curve shapes through mathematical equations.
This tutorial will explain the process in generating your own TPMS variations using Rhino 3D and the Grasshopper plugin. Rhino software does cost money for a licence, and if you'd rather download from an existing range, I've uploaded 44 variations for download on MyMiniFactory here.
One of the more popular TPMS, the gyroid shape, can be added as 3D printable infill with the new Slic3r infill, and is often used because it has a high strength to low filament usage ratio.
Grasshopper Plugin (Comes already with Rhino 6)
With these installed, you'll be able to open the Grasshopper Algorithm file I've created for generating the TPMS structures.
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Step 1: Open the .gh File
After opening the .gh file, you'll be able to see the drag and drop style algorithm. To create different types of TPMS, 'plug-in' a new type of equation by changing the starting connection point. You'll be able to change the thickness of the generated model and other factors through the number sliders.
Highlight half the components and select 'bake' to bring the model into being on the rhino workplane (see screenshot above).
That's all there is to it, enjoy!