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16.February.2011 the 47th day generates cv#47, Decimal Quadruple Beseige. Two moves a turn might be considered here for subvariant. There are so many pieces because the King can never be cornered, and in fact all pieces always have 8 adjacent squares -- same as to say each square has 8 squares adjacent, even if ostensibly at an ''edge.'' There is no edge. All the piece-types are regular because Ace is just Amazon. 'a6' joins to 't6', and so on, like a Cylindrical board. Player does not need to think of Torus or Torus with twist to understand the rest of the connectivity in order to play. For example, Pawn-e9 proceeds along one rectilinear pathway without capturing e9-e10-p1-p2-p3, where he promotes, assuming 'p2' and 'p3' had already cleared out. Gilman in the last comment describes Torus with a Twist, made after the evident Cylindrical board is formed, to complete the D.Q.B. connectivity. Think of extremely long cylinder, and instead of joining t1 to natural counterpart t10, twist 180 degrees, more or less, and then join to make the one finished Torus/donut intended here, by putting t1 orthogonally adjacent rather a10, s1 to b10, r1 to c10 and so on. Or is it in order k10, l10, and m10? What becomes is not an imaginary object at all but real board still having its entire surface covered, or accounted for. However, the playing surface is best visualized by human players exactly the way pictured in the article, not intruding functional 2-d board into 3-d perspective. (Pawn may have added capture mode not yet clear, so above subject to revision.) This cv for clarity, Gilman needs to reference some actual cells not just define leap lengths, which in the text are not all compatible with this account. There are other earlier cvs of related board concept that are better to learn before D.Q.B. of year 2009, and then D.Q.B. can be rated.

I've finally realised what kind of topology Quadruple Besiege boards have. It's a torus with a twist. If you join the array shown end to end to form a cyclinder, you then curve the cylinder further as if to make a normal torus, but twist one end by 180° just before actually making the join. Not a Moebius strip, not a Klein bottle, but a torus with a twisted tesselation.