Today we used Tinkercad to design 2D nets that fold up to regular 3D polyhedra, specifically the tetrahedron, octahedron, and icosahedron which all have triangular faces.
STL file: http://www.geekhaus.com/makerhome/day44_triangularnets.stl
Tinkercad link: https://tinkercad.com/things/66ZiQ7gjVMl-day-44-triangular-polyhedral-nets
Thingiverse link: http://www.thingiverse.com/thing:163459
Settings: Makerbot Replicator 2 on “Standard”, which is .2mm resolution, in 11 minutes for the tetrahedron, 22 minutes for the octahedron, and 38 minutes for the icosahedron.
Technical notes: The nets are made to have .2mm (one layer) base thickness plus another .2mm (another layer) for the faces themselves, which are inset just a bit from the base layer so that fold lines develop naturally. Thicker nets did not fold very well and tended to snap along the edges.
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I've also played around with some 2D nets folded into 3D shapes to support one of the VA Geometry SOLs. I can confirm that 0.2 mm layer heights seem to be a sweet spot for folds. One of the issues that comes up is when the first layer infill pattern is rectilinear, ie. a series of parallel threads of filament. Ideally these infill threads would be perpendicular to the fold for maximum strength but with the tetrahedron base unit, at least one fold is parallel or nearly parallel to the infill threads. In Slic3r, I am able to choose concentric infill which for the tetrahedron makes all the infill threads more perpendicular to the folds.
I normally use a Printrbot but I've also printed a foldable cube on the Makerbot and had problems with splits along the folds due to parallel infill. By rotating the flat shape I was able to get longer lasting folds as the infill angle to the fold was changed. Unfortunately when I tried to go a full 45 degree rotation Makerware again made the infill parallel.
All this to day that having higher edges is nice when gluing together the shapes so that you then use them as subunits in larger assemblies.
Here are some examples: http://www.thingiverse.com/thing:80348, http://www.thingiverse.com/thing:78075, http://www.thingiverse.com/thing:75093 and http://www.thingiverse.com/thing:116184
Definitely agree about the infill direction! And I *love* your Star Tetrahedron (thing 80348). So beautiful!