Octahedron Fractal plus tetrahedron

thingiverse

Updates on 20190626: I've attempted a new version generating two polyhedrons inside another, and it seems okay for three iterations but still has gaps not properly filled after four iterations. Please let me know what you think went wrong. ===================================================================================================================== As I pondered whether we could replace the Octree in Voxel to represent non-cubical spatial point positions, I realized my ignorance about polyhedrons led me to naively think a tetrahedron representation would reduce itself, resulting in a shifted point cloud representation. Then, when trying to visualize placing a tetrahedron inside another, the center result was an octahedron. This led me to discover an interesting octahedron fractal model while searching online, and I wondered if I could fill in the gaps. After conducting some research, I found numerous references online, including http://www.matematicasvisuales.com/english/html/geometry/planenets/octahedronnet.html: * 1 tetrahedron equals four tetrahedrons plus one octahedron * 1 octahedron equals six octahedrons plus eight tetrahedrons So, I attempted to write an iterative process to fill in the blanks (still not complete). However, the result is still intriguing. I failed to fill in the tetrahedrons on each surface, as shown in the capture. To print the model, since I generated it in the wrong orientation, you'll need to rotate it first. You'll have to rotate the 1st axis by 45 degrees and the 2nd axis by atan(1/sqrt(2)) around 35.2644 degrees to lay it flat (for my slicer, the 1st axis is x, and the 2nd is y). Problem with the model: * Overlapping generation isn't handled * Using hull to draw volume wireframes results in slow model generation, so I wasn't able to test iteration = 4 Future improvement: * Use a more efficient way of calculating connections that avoids overlapping generation * Correctly fill in the blanks (tetrahedrons as marked in the screen cap)