Sierpinski Tetrahedron

by dreameredeemer, published

Sierpinski Tetrahedron by dreameredeemer Mar 12, 2011

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These are Sierpinski (pronounced sherpinski) tetrahedrons from order 0 to order 4. Each was derived from George Hart's original order 5 model (found at www.georgehart.com/rp/rp.html) by taking advantage of the self-similarity that characterizes fractals and simply removing successive layers. This was my very first adventure with Blender, otherwise I would have made the models scale invariant, as the iterative construction generally implies. I put these together because the original order 5 model is too empty to print when scaled to fit on the ABP. Interesting note: when the first layer composed of order 1 tetrahedrons is finished, the print is about half done, despite this only making up about 13% of the total height. Sincere thanks to George for freely providing such beautiful mathematical models!


Warning! The order 4 model is scaled to use as much of the ABP as possible--be sure the wiring on the front right of the platform is secured close. Print with caution. Order 4 barely prints with a stepper driven extruder; at the given scale, expect these to be rather fragile... OTOH, a broken order 4 model becomes 4 order 3 models, so all is not lost.

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Very nice! For smaller scales (i.e. smaller then 10 cm on height) I had to strenghten the critical connections by making them thicker when printing upside down pyramid. Otherwise my printer brakes it.

Wow, impressive print. Did you use a stepper extruder?

Definitely, though I haven't done any tuning for the MK6, nor have I done any cleanup for fear of breaking it. It might print with a DC extruder, I figure there's some chance all the ooze would give it more structural support for the many spans, resulting in a sturdier product post cleanup. Pure outlandish speculation though.