40 "squares" chessboard

    Pictured below is an idea I invented in April 1999: a chessboard
of 40 "cells."  (You can call them squares, but the official term
is "cell.")  Each cell is a pentagon.

    A simple version of this can be visualized by taking two 12-sided,
regular dodecagons -- as are sometimes sold with 12-month calenders
printed on them -- and "pasting" them together where two faces meet.
(For real models use masking tape unless you're prepared to perma-
nently 'ruin' your originals!)  Note: Gaming stores sell dice of
this shape as well as several other unusual shapes.

    The result is a 20-cell chessboard, not counting the top and
bottom surfaces.  There are four rows (horizontals) of five cells
each, and the rows are continuous.  That is, there are no "sides"
to the chessboard, so the rows and movement of chess pieces along
those rows are said to be "cylindrical," like a chessboard drawn on
a tin can.

    Now put four such dodecagons together and the result is 40
cells, with 8 rows of 5 cells each.  The top and bottom faces, which
could be defined as used for special purposes, bring the total to
42.

                                      .
                                    .' `.
                                  .' top `.
                                  :surface:
  ................._______________:_______:_______________.........
  :(d8)   :(e8)   |a8     |b8     |c8     |d8     |e8     |(a8)   :
  :       :       |       |       |       |       |       |       :
   `.   .' `.    /^\     /^\     /^\     /^\     /^\     / `.   .' `.
     `.'(e7) `./a7   \./b7   \./c7   \./d7   \./e7   \./(a7) `.'(b7) `.
      :       |       |       |       |       |       |       :       :
      :.......|_______|_______|_______|_______|_______|.......:.......:
      :(e6)   |a6     |b6     |c6     |d6     |e6     |(a6)   :(b6)   :
      :       |       |       |       |       |       |       |       :
    .' `.   .' \     /^\     /^\     /^\     /^\     /^\    .' `.   .'
  .'(d5) `.'(e5) \./a5   \./b5   \./c5   \./d5   \./e5   \.'(a5) `.'
  :       :       |       |       |       |       |       |       :
  :.......:.......|_______|_______|_______|_______|_______|.......:
  :(d4)   :(e4)   |a4     |b4     |c4     |d4     |e4     |(a4)   :
  :       :       |       |       |       |       |       |       :
   `.   .' `.    /^\     /^\     /^\     /^\     /^\     / `.   .' `.
     `.'(e3) `./a3   \./b3   \./c3   \./d3   \./e3   \./(a3) `.'(b3) `.
      :       |       |       |       |       |       |       :       :
      :.......|_______|_______|_______|_______|_______|.......:.......:
      :(e2)   |a2     |b2     |c2     |d2     |e2     |(a2)   :(b2)   :
      :       |       |       |       |       |       |       :       :
    .' `.   .' \     /^\     /^\     /^\     /^\     /^\    .' `.   .'
  .'(d1) `.'(e1) \./a1   \./b1   \./c1   \./d1   \./e1   \.'(a1) `.'
  :       :       |       |       |       |       |       |       :
  :.......:.......|_______|_______|_______|_______|_______|.......:
                                  :bottom :
                                  :surface:
                                   `.   .'
                                     `.'

    In real life the cells are intended to be regular pentagons, but
the two-dimensional ascii version above isn't exactly like that.
Nevertheless, it has merit in making the concepts more easily vis-
ible.  And it's amazing how close one can get to "accuracy" with this
typewriter art.

    In this diagram the 40 *real* cells are shown with "solid" lines.
The dotted cells at the sides are shown merely for the sake of con-
venience to demonstrate the cylindrical nature of the chessboard.
They represent cells at the other end of the row, just to show
that horizontal movement would be continuous.  Thus the notational
designations for the dotted cells are given in parentheses.

    Using standard chess notation (a.k.a. algebraic notation), the
bottom row is the first rank; the second row is number two; and so
on, up to the top row which is the eighth rank.  In chess diagrams
the "white" pieces start at the bottom and move upward; the "black"
pieces start at the top and move downward.  The player with the
white pieces would be at the "bottom" end of the board; the player
with the black pieces would be at the "top" end of the board.

    This chess variation was originally intended to be submitted in
an annual contest run at that time by the sponsor of the chess vari-
ants website.  That year was expected to have a contest for inven-
tions using 40 "squares."  I don't think I ever finished writing up
the details for playing a game of essentially "regular" chess on
this board, so the idea never reached the contest.  I believe this
board and the ideas involved with it are being made public for the
first time here on this newsgroup.

    As in the case of my Lotus Chess game, my intention was to trans-
late the movements of regular chess pieces to this 40-pentagon en-
vironment.  That's too dull for some people's taste, but each kind
of tesselation brings with it some odd and interesting ramifications.
I doubt that I'll ever put time into developing games for use on
this board, but maybe someday other players or inventors will do so.

    --David Moeser
      Cincinnati, Ohio
-- 
         >>>----------------------------------------------<<<
         >>>      david moeser -- erasmus39 on yahoo      <<<
         >>>            Censornati, Ohio - USA            <<<
         >>>----------------------------------------------<<<
         *      "It isn't like regular chess, is it?!"      *