Start with space filling models of the Archimedean and Platonic Solids |
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Then, convert the space filling to wireframe approximations by changing every edge to a beam. All of the polyhedra are resized to the same bounding box and the same material volume. Thus the strut diameter and length of struts varies with each polyhedra (due to strut number) but they all contain the same material volume. | ||||||||||

A: space filling truncated octahedron. B: wireframe truncated octahedron within the same bounding box.
Note: these wireframe polyhedra are very similar to the open celled microstructures that exist in nature, shown at right. |
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So, we end up with a libray of architectures. This is taken from a manuscript, obviously, most of these are not based on Platonic/Archimedean solids. But the plumber's nightmare is based off somthing very simitlar to the minimum surface configuration page that you sent me. | ||||||||||

Finally, run some FEA on the architectures to determine their mechanical properties. | ||||||||||

The results indicate that there is a great difference in the modulus of these shapes solely as a result of architecture. Remember, all of these architectures contain the same amount of material, it has only been arranged in a different configuration. First graph, the results of increasing the porosity of one architecture. Second graph, all at 80% porosity. | ||||||||||

Next: onto rapid prototyping of the architectures | ||||||||||