Thursday, December 25, 2008

A beaded trefoil knot?

A jar of beaded fullerenes and nanotori

From Dec 25, 2008

Torus, torus, torus everywhere

From Dec 25, 2008

Sculpture outside the physics department, NTU.

A new type of helically coiled carbon nanotube

This HCNT consists an octagon and two pentagons in each unit cell.
From Dec 25, 2008

A huge helically coiled carbon nanotube

From Dec 25, 2008

Yet another beaded buckyball (YABB)

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.

D-type triply periodic minimal surface

From Dec 25, 2008

Another HG fullerene with Icosahedral symmetry

From Dec 25, 2008

High-genus structures

From Dec 25, 2008

From Dec 25, 2008

From Dec 25, 2008

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From Dec 25, 2008


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.

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

"Classification of Carbon Nanotori" accepted in J. Chem. Inf. Mod.

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)


Thursday, December 18, 2008

Helix with 5-8 pairs


C60 and C80

C20 again

truncated cube

truncated octahedron


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.

Small Sierpiski beaded fullerene

(created by Q.-R. Huang)

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)

Smallest High-Genus Beaded Fullerenes