Third level Sierpinski superbuckyball: C20⊗C20⊗C20

As was asked by Bih-Yaw, I think in principle one can always go on the process of using fullerenes to construct superfullerene, and then treat the result as the new module to build a supersuperfullerene etc.. The idea is the same. The problem is always physical limitations: the structure goes too heavy to support itself or you run out of memory trying to build that on a computer. Here is the simplest nontrivial case that I can do on my laptop, a third level superfullerene C20⊗C20⊗C20.

C20⊗C20⊗C20 with g=(1,1): C15920 (Ih)

It is clearer to see when there are only two adjacent nodes:

I would say this is not unbeadable. However, as mentioned, one has to make sure the structure is strong enough to hold itself up. In my experience the best shot is to go with 3mm plastic beads and 0.4mm fish lines, which I'm currently using for the construction of a C60⊗C60 superfullerene. Other possibilities are icosahedron⊗icosahedron⊗C60 or cube⊗cube⊗C60, but I think they are not as representative and illuminating as this one.

Clathrate cluster

I bought some more green rice-shape beads last week and managed to finish this interesting clathrate cluster of 60 dodecahedra in the last weekend. One can still see deformation of many dodecahedra in this clathrate cluster though.

Buckyball made of 60 dodecadedra

I made this structure with beads last weekend. Still unfinished. The finished structure should have 60 dodecahedra arranged like a buckball. One has two ways to interpret this structure:
1. If every dodecahedron represents a carbon atom, we have a standard C₆₀.
2. If we still use beads to represent CC bonds, then we have a giant molecule, C₇₅₀. In this molecule, 450 carbon atoms are sp³ hybridized or tetra-valent and 300 atoms are sp² hybridized or trivalent. But I suspect these sp² hybridized carbon atoms are not energetically favorable, so it is better to have hydrogen atoms connected to these sp2-carbons. Then we get C₇₅₀H₃₀₀!



The bead model of this structure (see here) might be first constructed by Emilie. She asked me to comment about this structure in my blog long time ago (I couldn't find the exact location though).

I decided to make one from beads after I saw the same structure made by a toy designer, Dick Esterle, who actually invented this kind of toys, in the Bridges conference last week.