Wednesday, February 29, 2012

C84 with three and four heptagonal holes

As I said in the previous post, one can puncture holes on a C84 and use the resulting structures as basic units for building larger graphitic structures. Here I show two C84-derived bead models with three and four holes surrounded by heptagonal.
The Schlegel diagram and a simple beading path for three-hole structure can be worked out easily.
Similarly, here is the Schlegel diagram and a beading path for a four-hole (tetravalent) unit.

Of course, one can use these building blocks to make many interesting structures. I am planning to make a dodecahedron consisting of 20 tetravalent units. It is not hard to see the angle between two holes in a unit is about 109 degree which is very close to 108 degree for the inner angle of a pentagon. So one can expect that these units should be happily fitted in the resulting dodecahedron without too much distortion.

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