Truss models of cubic and hexagonal closest packings

I made two more bead models of two-layer cuboctahedron and twisted cuboctahedron (anticuboctahedron) to illustrate the vector equilibrium of Buckminster Fuller. Through these two models, the connection to the cubic and hexagonal closest packings can also be visualized more easily.

Two icosahedral complexes derived from an icosahedron

Starting from a bead model of icosahedron, one can make a few beautiful rigid polyhedral complexes by adding more regular octahedra and tetrahedra surrounding the central icosahedron. Here are two examples:

Icosahedron + Icosidodecahedron

Icosahedron + Icosidodecahedron + Rhombic Hexecontahedron

Four bead models for the Bridges 2014 Seoul

The very first day of Bridges 2014 for setting up the mathart exhibit:

Horibe, Chia-Chin and I are going to have workshop, From Sangaku Problems to Mathematical Beading: A Hands-on Workshop..., for this meeting this afternoon.

Workshop at BCCE, Grand Valley State Univ.

I will give one more workshop in the 2014 Biennial Conference on Chemical Education which is hosted by the Grand Valley State Univ, Michigan next week. My workshop is arranged in the afternoon (2:00-5:00PM) of Aug. 4.

It is free. Hopefully, I brought enough beads with me for every participant.

"Mathematicians Solve The Topological Mystery Behind The “Brazuca” World Cup Football Just in time for the World Cup final"

I just noticed that there is a page from Medium - Everyone’s stories and ideas,
Mathematicians Solve The Topological Mystery Behind The “Brazuca” World Cup Football Just in time for the World Cup final,
which reported the manuscript, From the "Brazuca" ball to Octahedral Fullerenes: Their Construction and Classification, Yuan-Chia Fan and I submitted to the arXiv at the end of last month.

In fact, Yuan-Jia has been working on the general structural rules for this peculiar family of generalized fullerenes with octahedral symmetry for a period of time. When the FIFA World Cup started in the mid June, I noticed quite accidentally that the official soccer ball, the “Brazuca”, for the FIFA World Cup held in Brazil this year has exactly the same octahedral symmetry. Then, we rewrote the draft a little bit and changed the title to its current form. However, the manuscript was first rejected by the Journal of Chemical Information and Modelling because the paper is not of general interest to the readers of the journal. And then it was rejected again by the Journal Physical Chemistry A because the editor thought this paper falls outside the bounds of the journal.

Instead of finding another journal, I decided to put it in the print archive, arXiv, at the end of June. So people might find it interesting during the World Cup season.

The evolution of the official Adidas Soccer Balls since 1970.

In addition to the page on Medium - Everyone’s stories and ideas, I also noticed three more pages which refer to the Yuan-Jia's work on the octahedral fullerenes and their connection to the Brazuca:

• Physics World: Molecular footballs, knotty headphones and a naming contest for exoplanets.
• Brazuca, la scienza a servizio del calcio (Italian)
• Il Brazuca e i ‘misteri topologici’ dietro i palloni dei mondiali (Italian)

Workshop for the NTU CampCamp

The first few slides and a few photos from the workshop I had for the NTU ChemCamp this afternoon in the Chemistry Building of National Taiwan University: