The geometry of the Double Gyroid wire network: Quantum and Classical

We discuss a novel nano material structure of a Double Gyroid (DG)
wire network. We start by introducing the geometrical structure of the DG
and its
fabrication as background. We then use methods of commutative and
 non-commutative geometry
to describe this quantum wire network. Its non--commutative geometry
is closely related to non-commutative 3-tori as we discuss in detail.
This is joint work with R. Kaufmann and S. Khlebnikov.