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Descrição
The Menger Sponge is the 3D analogue to the Sierpiński Carpet fractal.
3D print a Menger Sponge in its usual orientation is difficult because it requires many internal supports that might be hard to remove.
Cutting the Menger Sponge in half through a plane perpendicular to one of its main diagonals makes this model trivially easy to print without supports (nor infill!). Moreover, the cut generates a set of 6-pointed stars arranged in a self-similar pattern.
There are, indeed, many other diagonal cuts, that can be used to print this model without supports, which are also quite interesting from an aesthetic point of view.
In this repository you could find a really complete set of such pre-cut Menger Sponges and the parametric OpenScad script used to generate them.
Printing recommendations
All models are scaled so they belong to the same 100mm x 100mm x 100mm cube (= 1 liter). You can scale them in all 3 dimensions to get smaller cubes (the ones in the pictures are scaled at 60% to get 60mm x 60mm x 60mm cubes).
Menger 0 is just a cube, and the pre-cut models can be printed in vase mode to save time and material. They might be useful to explain some less-obvious cube sections, like the equilateral triangle or the regular hexagon.
Menger 1-3 are the first 3 iterations of the Menger Sponge (the Menger Sponge fractal is the limit, when N tends to infinity, of this family of figures), and the pre-cut models can be printed in the given orientation without supports. Moreover, they can be printed without base-layers nor infill, providing a clear view of the inside of this fractal (see pictures).
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