45° sectioned Level 2 Menger Sponge

thingiverse

This is my 45° sectioned Level 2 Menger Sponge. There are many like it, but this one is ours. Constructed by intersecting 3 2D gaskets, the OpenSCAD code is probably more interesting than the thing. I've also included a 2D gasket of this design projected onto the XY plane just because it's pretty. This thing was designed and printed at Protolab in Toronto. Print Settings Printer Brand: Printrbot Printer: Simple Black Rafts: No Resolution: 0.25 mm Infill: 20% Notes: Test printed using dark blue PLA at 195°C. How I Designed This This model is constructed in OpenSCAD a little differently from most Menger cubes: generate a cube of side s, centre [ ½s, ½s, ½s ] with Sierpinski gasket holes “drilled” parallel to the Z-axis by extruding a square that has had 9 holes cut from it draw three of those extruded Sierpinski cubes, each one translated to be parallel to the X, Y and Z axes; intersect those three extrusions to make a Menger sponge; translate the Menger sponge to be centred on the origin; rotate the centred Menger sponge to be on point; (which is not a rotation of [ -45°, -45°, 0 ], as one might naïvely assume …) draw a suitably big shape whose top surface is the XY plane; (I chose a cylinder of radius and height s, centre [ 0, 0, -½s ], but you might choose differently) subtract the suitably big shape from the Menger sponge, leaving a section with 7 six-pointed stars. (aka Shatkona / Kagome / מָגֵן דָּוִד / خاتم_سليمان)