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Sam Trenholme wrote on Tue, Mar 1, 2005 08:43 AM UTC:
I think the idea of generalizing chess to non-standard tessellations is an interesting one. How does one play chess on a Penrose tile tessellation, for example? Unlike Go or <A href=http://arimaa.com/arimaa/>Arimaa</A>, where the tesselation can change without otherwise changing the rules (<A href=http://www.di.fc.ul.pt/~jpn/gv/boards.htm>see here</A>, for example), a new tessellation of chess requires a new set of moves for the pieces. <p> One interesting game is <A href=http://www.chessvariants.org/shape.dir/parachess.html>parachess</A>, which uses an interesting tessellation to play chess with. <p> Even the triangle tessellation is pretty rare, such as with <A href= http://www.chessvariants.org/shape.dir/klinzha/klinzha.html>Klin Zha</A> and <A href=http://www.chessvariants.org/44.dir/sankaku-shogi.html>Sankaku Shogi</A> (Thanks, Mr. Howe, for pointing these out). Of course, <A href=http://www.chessvariants.org/38.dir/crazy/crazy38s.html>crazy 38s</A> uses a somewhat different tessellation. <p> Does anyone know any other chess variants that use non-standard (read: non-square and non-hex) tesellations?

George Duke wrote on Tue, Mar 1, 2005 05:41 PM UTC:
Circular chesses, though square-based, create different patterns. For ex.,
Round Table 84 has triangular areas and also characteristics of Cylinder
Chess. All sixty hexagonal CVs here can keep their same rules and
subdivide each cell into six triangles adding connectivity for (rare)
special move(s); this can be visualized in Shankaku Shogi drawings. Most all the 
2000 CVP games actually have squares divisible into two isosceles right triangles, 
so would be playable  with rules unchanged plus special-move feature based on triangular 
subdivision and orientation.  Squared and hexagonal areas could also be combined in 
game boards, regardless discontinuity in tesselation. It would be no more 
distracting than Ultra-Slanted Escalator's having regions with squares offset.

George Duke wrote on Fri, Mar 4, 2005 02:36 AM UTC:
Weave & Dungeon(81 squares)by Dan Troyka 2002 has unusual connectivity and
perfect symmetry. Among six piece-types specially suited for its 
'weave' board, a sort of counter-tesselation, Triangles > Square > Pentagon >
 Circle in value.

George Duke wrote on Fri, Sep 19, 2008 10:56 PM UTC:
Sam, Penturanga with pentagons wins contest in 2008, well, over 3 1/2 years
after your original question as to non-standard non-square non-hex. Unorthodox tesselations in Chess can be seen as avant garde like cubist art of Picasso or Braque. ''Also, the milieu of chess players is far more sympathetic than that of artist. These people are completely cloudy, completely blinkered madmen, of a certain quality, the way an artist is supposed to be and isn't, in general.''  -- Marcel Duchamp (1968), artist & chess player

Joe Joyce wrote on Thu, Sep 25, 2008 09:05 AM UTC:
The unorthodox tessellation of Penturanga, coupled with a fine piece
choice, allows this game to play 'larger' than its 46 square size. The
game has the feel of standard chess on an unorthodox board. It does not
have the feel of a mini-version of chess. This is why it won the contest.
Arguments as to whether it was 'really' a hex board were irrelevant to
the decision. The strange board worked against Penturanga initially; it
was difficult to follow the piece moves at first. But the effects of the
board on gameplay overcame... hmmm, overcame the effects of the board on
gameplay! :-) Once you get past the strangeness, the game is good. Getting
past, though, takes a little effort. The board is simultaneously the
game's best and worst feature.

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