  As noticed in 2006 by the author of the present article, 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 sharing a remarkable symmetric property with
the diamond crystal, thus deserving to be called the diamond twin although
their shapes look quite a bit different at first sight. In this short note, we
shall provide an interesting mutual relationship between them, expressed in
terms of ``building blocks" and ``period lattices." This may give further
justification to employ the word ``twin." What is more, our discussion brings
us to the notion of ``orthogonally symmetric lattice," a generalization of
irreducible root lattices, which makes the diamond and its twin very distinct
among all crystal structures.
