04.06.2019; Kolloquium
SFB-Kolloquium Sunada
(Meiji University)
Diamond twin revisited
As noticed in 2006 by the speaker of the present talk, the hypothetical crystal---
described by crystallographer F. Laves (1932 ) for the first time and designated „Laves'
graph of girth ten“ by geometer H. S. M. Coxeter (1955)---is a unique crystal net with a
remarkable symmetric structure similar to the diamond crystal, thus deserving to be
called the diamond twin although their shapes look quite a bit different at first sight. In
this talk, I shall observe an interesting mutual relationship between them, expressed in
terms of “orthogonally symmetric lattice“, a generalization of irreducible root lattices.
This may give further justification to use the word „twin“.