Tuesday, April 13, 2010

Procedure of creating a high-genus fullerene

Here are a few pictures of another high-genus fullerene I made last month. This structure contains 12 necks, each of them is made of 5 octagons again.
To make this molecule, I have used approximately six long threads with around 4 meters each.

It is clear that we have to weave the inner part of a HG-fullerene first, in this case, 12 necks connected to each other.

Note also that this structure is, I believe, one of the two simplest high-genus fullerenes with icosahedral symmetry one can create. Another icosahedral HG-fullerene has 10 heptagons in each of 12 necks.

Friday, April 9, 2010

Space-Filling Polyhedra Based on a Truncated Octahedron

I made this structure during the spring break. Chuang has made a similar structure with several truncated octahedron before. But his structure has three unit cells separated connected. So the first unit cell is not connected to the third unit cell directly. My original goal is to make a structure with six unit cells connected to each other, something like a 2x2x2 cluster. However, the structure seems to be sensitive the small deviation at each local connection. Although truncated octahedron can fill the space. the structure I made seems to have pretty large strain and distorion.

Thursday, April 8, 2010

Octahedron with six nodes on each face

Rhombic dodecahedral honeycomb

It is well known that one can tile the space using the rhombic dodecahedron as a unit cell. The resulting structure is the so-called the rhombic dodecahedra honeycomb.
Check wikipedia,http://en.wikipedia.org/wiki/Rhombic_dodecahedral_honeycomb, for more discussion.

I made a physical model of this structure with beads during the spring break.

Tuesday, April 6, 2010

Another set of beaded models of platonic solids

Here is another set of beaded Platonic solids made with the same type of beads.

Another Rhombic dodecahedron

I made this rhombic dodecahedron a few days ago.

Au20: a molecular tetrahedron

It is known that the geometry of an Au20 cluster is a tetrahedron with all of 20 gold atoms on the surface. It is quite straightforward to make this structure with beads. Since most of gold atoms in this structure have coordination higher than 3, so I have chosen rod-shaped beads. The resulting beaded structure seems to mimic the tetrahedron shape pretty well.