Thursday, November 1, 2012

The procedure for constructing G- and D- surfaces

Here are a few slides that show the detailed instruction for making G- and D- surfaces, which I prepared for students and teachers of TFG (Taipei) school. As I said it could be a difficult task because the gyroidal structure and D-type TPMS are complicated structures. The first bead model of a 2x2x2 G-surface took Chern and I almost five years to finally make it. Of course, I have many unfinished bead models of this structure or similar structures with different Goldberg vectors, some made by Chern and some by me, which have mistakes here or there.

In order to how to make this model successfully, we'd better to know the three-dimensional structures of G- and D-type surfaces a little bit. Additionally, it is crucial to know how two structures can be decomposed into several basic unit strips and how to connect these helical strips.

I am also working on an article in Chinese entitled "大家一起動手做多孔螺旋與鑽石型三度週期最小曲面的串珠模型 (A Hands-on, Collaborative Approach to Gyroid- and Diamond-type Triply Periodic Minimal Surfaces with Beads)", which describes in details the procedure to make G- and D-surfaces and also give some background information on TPMS. I might be able to finish the paper in a few days. Hopefully, I will find time to do it in English someday. But, even without detailed explanations, these slides together with other posts in this blog should already contain enough information for people who want to do it.

The first nine slides should give students a better picture of a gyroid:
In slide 10, we can see how a coronene unit corresponds to 1/8 unit cell. Important structural features of a beaded gyroid is summarized in slide 11. Then in slides 12-15, I describe how to make the basic construction unit, a long strip, which should be easy for student to make.
The remaining five slides, 16-20, use schematic diagrams to show how two slides can be combined to generate either D-surface or G-surface.
To create a 2x2x2 gyroidal surface, we need 16 strips, which can be easily done if many people work in parallel. To connect them is nontrivial, you need to follow slides 16-20 carefully. In total, there are about 5000 beads in the model.

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