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Another question: how third player's rooks exactly moves?
Is it supposed that in this setup pawns of first two players promotes where non-pawn pieces of third player starts? It may be interesting setup for 6-player game.
The 14x14 board has always struck me as a bit unwieldy for just 64 pieces (hencr my own Fivequarters) - but might benefit from an extra player. A 3-player Reflection Teammate might look like this, where the third army are shown by the inverted White pieces to save characters:
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Daniil Frolov has solution recently well in 2010 in "Reflection teammate" for Missoum's poser of year 1997 to make a reflection or forced symmetrical Chess: Mirror. He links Missoum's game in lead sentence.
Charles Gilman's comment here is interesting: Three_Player. There Gilman lines up a Three Player version to be played by Reflection Teammate Rules. Academic game theory counterpart could be China, Russia and United States. In Charles' diagram the third force occupies the center entirely, so there is not only Reflection but potential cooperation two against one shifting alliance when there are three more or less equal.