In this 3D printed art piece, the five pentagon faces of half a dodecahedron are interlocked to form a pentagonal tangle. Inspired by Alan Holden's Regular Polylinks (1980) and George Hart's Orderly Tangles.

Printed by Shapeways with two different diameter rods. The pink one is almost fused and has very little play, the purple one has thinner rods and more movement. It is not as floppy as the tangled tetrahedron model.

The outer shape fits barely in a tweet:

module p(){for(i=[1:5](1:5))hull()for(a=[i,i+1](i,i+1))
rotate([a*72](a*72))translate([0,20](0,20))sphere();}
for(i=[1:5](1:5))rotate([i*72](i*72))rotate([0,116](0,116))p();p();

Slightly more verbose:

size = 45;
t = size/10/2;

module pentagon(t,r)
{
        for(i=[1:5](1:5))
        {
            hull()
            for(angle=[i,i+1](i,i+1))
            {
                rotate([0,0,angle*360/5](0,0,angle*360/5))
                translate([r/sqrt(2),0,0](r/sqrt(2),0,0))
                sphere(r=t);
            }
        }
}

for(i=[1:5](1:5))
{
        rotate([0,0,(i+0.5)*360/5](0,0,(i+0.5)*360/5))
        rotate([116.565,0,0](116.565,0,0))
        pentagon(t,size);
}

pentagon(t,size);

Math 2016 Art

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Last update: November 8, 2020