Icosahedron

Platonic Solids

I bought these elongated beads last week, on sale, of course. The shape of these beads are closer to that of chemical bonds. I have used these beads to create five Platonic solids. They look great.

Tetrahedron


Cube



Octahedron




Dodecahedron



Icosahedron

Proof: N5=N7 in TCNT

Proof: 12 pentagons in a fullerene

TCNT with 48 polygons

Chuang has also created a beaded model of TCNT with 48 polygon pairs:

TCNT with 58 polygons

It is easy to prove that the number of pentagons is twice of that of octagons:

Weaving code

Here is a slide I made for weaving code of C60, which I used for a talk yesterday.

C140 with 10 pentagons and 5 octagons

Chuang has also discovered a whole family of carbon tori consisted of 5 octagons in the inner-rim and 10 pentagons in the outer-rim. I do not exactly know if anybody has reported this kind of structures or not. But according to Chuang some Japanese should have known this type of structures, since they have described this kind of structures in a vague way.

The following picture shows the first beaded torus (with 140 carbons) belonging to this family. This picture is made by a scanner. It is not easy to see the inner-rim structure though.