Re: Proof the Torus is an equal goals game

Notes:

1. A hexagonally tessellated square can be formed into a perfect
cylinder and then formed into a torus, as you know.  A hexagonally
tessellated rhombus can be formed into an odd cylindrical shape, not a
perfect cylinder.  However the right end of that odd shape fits
perfectly into the left end.  Hence the rhombus can be used to create
a torus.  That torus will have the exact size and pattern as the one
created from the hexagonally tessellated square.

2. There is a well defined one to one mapping between EW loops on the
rhombus (oriented as shown) and EW loops on the square, but there's no
such well defined mapping between NS loops on the rhombus and NS loops
on the square, at least none that I could discover.  There are however
the same *number* of NS loops on both the square and the rhombus, as
was demonstrated in the proof.