Menger's Sponge (Fractal Cube, 3D Sierpinski's Carpet)

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Fractal cube known as Menger's Sponge (or 3D Sierpinski's carpet). This shape has infinite area and zero volume - it means very hard to calculate (time/memory) in higher order, and hard to 3D print-out. I could calculate up to 4th order using PC and 3rd order using cheap FDM printer. Expecting anybody challenge more!! How I Designed This I used cube.scad for OpenSCAD. This shape is famous because of explode of calculation/memory, so 3rd order was the limit. Another method is, generating fractal "corridor" (with cubedig.scad) copy & rotate into Z->X/Y axis direction, then subtract (boolean difference) from cube. However in this method, 4rth order was the limit. The "cubedig4-dig145.stl" is 145mm cube corridor (note: the corridor is a bit longer than 145mm). The result (resized into 1/3) is "cubedig4_48.33," generated by Blender. After these efforts, I found my 3D printer (Da Vinci) cannot print over 3rd order - density of the object is too low, and too fragile.