Chess and Chess
in a Toroidal Board may serve a hint for playing Byzantine Chess
on the torus shaped board.
As soon the edges of the circular board are joined a torus is constructed.
(The rules remain the same, only the geometry is changed).
Perhaps, the Byzantine Chess on the toroidal board has been experienced in Constantinople,
recently (1999-2001) it was considered by several mathematicians (among whom the present authors).
On account of exotic geometry this variant belongs better to the scope
of mathematics rather than sport or game.
But for playing for joy it is suited well.
The nominal strength of Bishops and Rooks does not depend
on the changes of geometry.
But a Rook on the toroidal board has circular motion either over the long 16-cell circle (as on the circular board) or over the short 4-cell circle:
The essential changes concern the Knights and
There are no edges on the toroidal board and both figures feel themselves quite well everywhere, while on the circular board their abilities are restricted at the edges.
On the torus shaped board all 6 squares are always available for the
and the Queen has all 4 squares
Perhaps, the most exotic is the Rook rotation along and across and
the Pawns phalanx with no edges at all (now the a-h pawns have two neighbors). .
Black has material advantage (the Knight for 2 Pawns) but position of his King is dangerous.
1. e6xh7++ (capturing across the glued edges) Ke8-f7 (the only move)
2. Rd1-e7+ Kf7-g6 (2. ... Kf7 x f6 changes nothing)
3. Rh1-e1 Bh6 (3. ... g5 x f4 is followed by 4. Re1-e6+)
4. Rg7+ Kxf6 (the only move)
5. Rg7-e7 g5xf4 (this prevents 6. Re1-e6#)
6. Re1-e6+ Kf6-g5
7. Re7-g7+ Kg5-h4 (the only move)
8. Re6-e4# (the Rook strikes from e4 on h4 since the edges are glued)