Cube Sculptures

Introverted and Extroverted Cubes

In the fall of 2007, I got interested in building 3D sculptures , mixing an organic feeling with the mathematical aspect of cubes.
I started by creating a pattern seen in many flowers:

magicAngle = Pi 137.5/180;
Centers2D = 
  Table[ Sqrt[n] {Cos[ n magicAngle], Sin[n magicAngle]}, {n, 1, 200}];
  Disk[#, .7] & /@ Centers2D
  ], AspectRatio -> 1

Then I turned every disk into a losange:

and extended the pattern to fill the square:

Then did a Delauney triangulation of the set of points, and gave it a smooth Z value

The removed the polygons which were inside the losanges

Duplicate the surface, and connect the edges, and the losanges internally..
It builds an extrusion really

Then, I just needed to connect the face six times, and add the extra edges… and we got the introverted cube

And doing the exact same thing with the faces oriented the other way, generated the extroverted cube

Some prints on the Zcorp printer

Cube printed in metal (with shapeways)

This one is made of steel and bronze

I also made some out of high resolution epoxy (earings)