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In reply to Tony Paletta's 'What would be an appropriate name for the unit White moved first?', the same could be asked about any of the pieces. It seems to me that they should all be called by their usual names as the board is really a square one in disguise. Only two orthogonals are being used as orthogonals. The other is being used as a diagonal, as is one root-3 axis. The two remaining root-3s and two of the four root-7s are being used as root-5s. A problem would only arise were pieces added that actually reflect the nature of the board - and then only as regards orthogonal moves - but each group of pieces when viewing the board as that of the other group would be more exotic than I am considering in this series.