standard dodecahedral structures and two-layer high-genus fullerenes.
He has intentionally pushed the vertices inward so one can see the possibility
of hole opening at that position.
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| From Dec 25, 2008 |
Saturday, December 27, 2008
Precursor of a high-geneus fullerene
Chuang made this beaded model in order to illustrate the connection between
standard dodecahedral structures and two-layer high-genus fullerenes.
He has intentionally pushed the vertices inward so one can see the possibility
of hole opening at that position.
standard dodecahedral structures and two-layer high-genus fullerenes.
He has intentionally pushed the vertices inward so one can see the possibility
of hole opening at that position.
Thursday, December 25, 2008
A new type of helically coiled carbon nanotube
This HCNT consists an octagon and two pentagons in each unit cell.
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| From Dec 25, 2008 |
Yet another beaded buckyball (YABB)
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| From Dec 25, 2008 |
Chuang made his model with 20mm (2cm) beads. These are largest beads we can find in the local store at Taipei.
High-genus structures
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| From Dec 25, 2008 |
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| From Dec 25, 2008 |
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| From Dec 25, 2008 |
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| From Dec 25, 2008 |
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| From Dec 25, 2008 |
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| From Dec 25, 2008 |
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| From Dec 25, 2008 |
C168
C168 is quite uniqe because it correponds to C60 in the hyperbolic space.
We can view standard fullerenes as a tiling of graphene sheet on a sphere, which is a two-dimensional manifold with postive curvature everywhere. C60 corresponds to the smallest fullerene with all pentagons separated by only one CC bond. Similarly, C168 is the smallest fullerene in a hyperbolic space with all heptagons separated by only one CC bond.
In the bead model I created, purple beads stand for the edges of heptagons, and white beads are the CC bonds separating different heptagons.
(I gave this model to Dirk Huylebrouck, a professor in the department of architecture at Sint Lucas (Brussels, Belgium) at the Bridges Pecs, Hungary 2010)
We can view standard fullerenes as a tiling of graphene sheet on a sphere, which is a two-dimensional manifold with postive curvature everywhere. C60 corresponds to the smallest fullerene with all pentagons separated by only one CC bond. Similarly, C168 is the smallest fullerene in a hyperbolic space with all heptagons separated by only one CC bond.
In the bead model I created, purple beads stand for the edges of heptagons, and white beads are the CC bonds separating different heptagons.
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| From Dec 25, 2008 |
(I gave this model to Dirk Huylebrouck, a professor in the department of architecture at Sint Lucas (Brussels, Belgium) at the Bridges Pecs, Hungary 2010)
Monday, December 22, 2008
Torus with tetravalent vertices
This amazing beaded structure is connected by a tetravalent network, which is different our previous trivalent beaded fullerenes. The construction rule for this type of toroidal systems, however, is exactly similar to that we used for carbon tori. But, instead of pentagons and heptagons, here we use triangle and pentagons to simulate the positive and negative Gaussian curvatures located in the outer- and inner-rim of the torus. Generalization to other topologically nontrivial 2-D structures seems to be straightforward.
(work by Chuang)
(work by Chuang)
Thursday, December 18, 2008
Tetrahedron
I try to experiment with the idea that using three beads to stand for an edge of polyhedron. In this case, I made a tetrahedron. Previously, I have posted some of this kind of models. The original idea came from Chuang again.
Precursor of a high-geneus fullerene
Here is an icosahedral fullerene in which the sharp vertices are forced innerward such that we can view this structure as the precursor for forming the outer part of a hight-genus fullerene. (created by Chuang)
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