Friday, August 17, 2007

On the weaving procedure for constructing a gyroidal graphnoid

After a careful examination of the arrangement of hexagons and octagons in Chuang's first model. I found a simple weaving procedure for the construction of a gyroidal graphenoid. This procedure consists of several rules for weavings:

Local rules:
1. Every hexagon is surrounded by six octagons. (see Fig. a)
2. Every octagons is surrounded by four hexagons and four octagons arranged in an alternant pattern.

(Since there are two types of CC bonds, 6-8 bonds and 8-8 bonds, so it is convenient to use two colors to represent these two different bonds)

Global rules:
3. ...? It is important. I only have a rough idea though. It is not very effective. Mistake can happen easily.

Global rules are hard to carry out. I spent several hours this morning. The resulting beaded gyroidal graphenoid is in fig. c. I have to confess that this beaded model is not particularly attracting.

The reason I'd like to find a geometry-independent weaving rules is that as long as we follow these rules, we can concentrate on weaving much more easily without paying attention to the 3D geometry information. Indeed in the weaving of the small fullerenes, I have found a general weaving rule based on the so-called spiral code.

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