Departament de Química Inorgànica
Centre Especial de Recerca en Química Teòrica (CeRQT), Universitat de Barcelona
Nesting of fullerenes and Frank-Kasper polyhedra: The duality relationship between fullerenes and Frank-Kasper polyhedra suggests that these two families of polyhedra appear nested in solid state structures. Magic numbers, described by simple mathematical relationships, identify four families of fullerenes with tetrahedral and icosahedral symmetries.
First email: Tue, Jul 9, 2013 at 6:29 PM
Dear Prof. Dr. Santiago Alvarez:
Your work is so substantial and focused. Thank you for all that you have done and for your vision to explore the very nature of structure. Given your earlier work at Cornell (and throughout the USA), I’ve made the assumption that it is OK to communicate in English. My 5th-grade Spanish obviously would not work!
Within a few weeks my wife and I will be in Barcelona. Our trip begins in your city for many reasons. I am a television producer as well as a person interested in nature of structure, particularly Frank-Kaspers work of 1959 that focused on the five regular tetrahedra around a shared edge. I write to see if you have done any analysis of the 7.36 degree gap (a). Within the Chrysler logo, the Pentastar, that gap is distributed over the five edges. According to John Conway and others, within the twenty regular tetrahedra about a shared vertex (an icosahedron), the gaps amount to 1.54 steradians (b).
I would like to make some references to your work for a rather simple construct that we discovered in a high school geometry class. We have been building simple constructions from the smallest number of vertices and we are looking for more references to that simple Frank-Kasper poly-tetrahedral structure.
If you are in Barcelona the first week of August, I would be pleased to meet you, even if just briefly. Thank you.
PS. Are you familiar with Mysteries in Packing Regular Tetrahedra” Jeffrey C. Lagarias and Chuanming Zong?