Friday, June 4, 2010

2x2x2 bead model of Schoen's I-WP surface

Chern Chuang (莊宸) created this amazing graphitic structures consisting of a Schoen's I-WP surface decorated with graphene sheet. The I-WP surface, found by Schoen in 1970, is a TPMS of cubic symmetry Im3m. In addition to I-WP surface, there are other TPMSs of Im3m symmetry, such as Schwartz P and Neovius surfaces.

Chuang figured out the systematic structural rule for this kind of periodic minimal surface at the beginning of this year. Based on his post, I constructed a 1x1x1 bead model for this structure using three different colors of beads. Apparently, he seems to find time to bead even in the army. Now we have this beautiful 2x2x2 bead model created with 5mm semi-transparent plastic beads. Based on the previous post by Chuang, there are 3456 carbon atoms in the structure. So one need about 5000 beads to create it. It is quite a work.

I am kind of surprised by the strong mechanical strength of this structure. Unlike bead models for other minimal surfaces including Schwartz P or D surfaces, this model seems to be quite rigid, and a little bit like that of a brick. So, it may not be a bad idea to have this kind of 2x2x2 I-WP surface as a high-strength but low-density brick for purpose of construction. The only problem is that it is quite difficult to create even just one of this kind of bricks. We may solve the problem if we can invent a robot to weave them automatically.

The 2x2x2 I-WP surface and my friend's iPad:

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