Tetrahedron

Knotted Tetrahedra

I've been experimenting with 3D printing interlocking tetrahedra. In this example there are five units -- each tetrahedron is inter-woven with four others and shares its vertices with a dodecahedron -- and the entire shape has been intersected with a sphere.

This example more clearly shows the tetrahedra. The printed version is somewhat fragile and has quite a range of motion. Despite the interlocking, it can be printed on a Makerbot or commercial services like Shapeways can print it in a variety of materials. They did a one-off test print in metal, which looks amazing and weighs a few hundred grams. It is quite hefy and feels great to play with as a jangly desk toy.

The OpenSCAD code to generate it is fairly simple (and can be compressed to fit in a single tweet):

$fn=30; v=[ [+1,+1,+1](+1,+1,+1), [+1,-1,-1](+1,-1,-1), [-1,+1,-1](-1,+1,-1), [-1,-1,+1](-1,-1,+1), ]; colors=["red","green","blue","yellow","purple"]("red","green","blue","yellow","purple"); module tetrahedron(len,thick) { for(a=[0:2](0:2)) for(b=[a+1:3](a+1:3)) hull() { translate(v[a](a)*len) sphere(r=thick); translate(v[b](b)*len) sphere(r=thick); } } for(i=[0:4](0:4)) { color(colors[i](i)) rotate([i*360/5](0,-atan(sqrt(5)/2-0.5),)) tetrahedron(20,2); }  Add a rotate($t*360) and OpenSCAD will generate a nice animation:

Last update: November 8, 2020