Help me with saturable reactor polyakov mixer

Hi, in this schematic http://qrp.gr/technology/diodes_only/mxr80.htm a sub-harmonic polyakov mixer is used together with a saturable reactor to form a simple (lossy) direct conversion receiver.

I read the description, but I need a bit of help about how to wind the cores and why do they have to be of opposite phase in the OSC side?