Modified Goldberg Polyhedra

A recent paper entitled "Self-assembly of tetravalent Goldberg polyhedra from 144 small components" (http://www.nature.com/nature/journal/v540/n7634/fig_tab/nature20771_F3.html) (published in Nature by Makoto Fujita et al.) described a kind of self-assembled molecular structures based on the so-called tetrabalent Goldberg polyhedra consisting of square lattice decorated with eight triangles.

Incidentally, Chern Chuang also constructed many bead models of this type while he was still a student at NTU. Every polyhedron of this kind possesses a unique Goldberg vector.

Previous post: Chiral cube - the generalized Goldberg polyhedra , in this post, a model of (3,1) Goldberg polyhedron is made.

Update: Equation of States for US Presidential Elections

I modified the figure a little bit to show the two forbidden regions in the 2nd and 4th quadrants, which are violated twice in the past US presidential elections now.

Update: Equation of States for US Presidential Elections

Updated with the newest data, Clinton 59,835,153 votes (228), Trump: 59,618,815 votes (279), from USA today. Like the 2000 election, the result this time fell again in the forbidden regions, the 2nd and 4th quadrants. The people of US should consider a new electoral system.

Previous post 4 years ago.

Frank-Kasper Polyhedra

Goldberg's tri-stable polyhedron

Zeolite PKU-12

I made a bead model for the zeolite PKU-12 and gave it to the chemistry college of Peking University as a souvenir when I was invited to Beijing last November.

MEP (Melanophlogite, Weaire-Phelan structure, Clathrate type I)

This model is accepted for the JMM 2017. (Nov. 11, 2016)

Sodalite (Kelvin structure, or Bitruncated cubic honeycomb)

For more description of this model, see the page from the Bridge conference 2016. (Nov. 11, 2016)

Zeolite A (Cantitruncated cubic honeycomb)

For more description of this model, see the page from the Bridge conference 2016. (Nov. 11, 2016)

數學串珠-繽紛多彩的奈米結構與幾何 (Mathematical Beading – Kaleidoscopic structures and geometries in the nano world)

Chiachin and I wrote a paper entitled "數學串珠-繽紛多彩的奈米結構與幾何" (Mathematical Beading – Kaleidoscopic structures and geometries in the nano world) for the special issue on the connection between math and art in Science Study (科學研習), a local science magazine in Taiwan. Here is the first page.

The pdf file can be found here.