Sunday, April 19, 2015

Circular helix winding around a central torus

Horibe-San just constructed another beautiful beadwork, a circular helical carbon nanotube (or circular carbon spring) winding around a toroidal carbon nanotube.

Friday, April 3, 2015

Bead model of the Chen-Gackstatter surface of genus 1

I made a bead model which approximates the minimal surface, Chen-Gackstatter surface of genus 1, for the spring break.
Other Chen–Gackstatter surfaces can be made with mathematical beading, in principle!

Thursday, March 26, 2015

Torus knot (2,9) by Kazunori Horibe

Kazunori email these photos of a beautiful bead model of (2,9)-Carbon nanotube torus knot (CNTTK) he just made the other day. To make the structure more clearly, I also use the Grapher to create the corresponding torus knot.

Wednesday, March 11, 2015

Hyperbolic soccerball

I posted many hyperbolic bead models before. But most of them are periodic surface structures in 1- to 3-D dimensional spaces. Examples are various periodic minimal surfaces. In these models, one needs to pay attention to the subtle periodic conditions in the course of beading. Sometimes, it makes the beading quite difficult.
Here, I show a simple construction of hyperbolic soccerball (truncated order-7 triangular tiling) consisting of infinitely many heptagons (blue beads), each of them are connected to seven neighboring heptagons by only one carbon-carbon bond, which is represented by a yellow bead in the model shown below.
Following the spiral beading path by adding hexagons and heptagons, eventually one obtains the hyperbolic soccerball, or more exactly a hyperbolic graphitic snowflake. There is no need to worry about the periodic conditions among different parts of the structure.
From wiki: Truncated order-7 triangular tiling
In principle, one can also use kirigami (paper cutting) to make a model of the hyperbolic soccerball. But I found that the beading technique is much easier for making robust structure of this object due to the nature of mathematical beading. Also the bead hyperbolic soccerball should be able to model the local force field of hyperbolic soccerball to certain extent because the bead model not just gives the connectivity of the molecular graph right, but also mimics the microscopic repulsions among chemical bonds.