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<P>With respect to the Thunderbird, this is what I visualized:</P>
<IMG SRC="/play/pbm/drawdiagram.php?code=1prnqb-----2p2bk----3p1b1n---3%7Bnstone%7D%7Bnstone%7D%7Bnstone%7D2r--3%7Bnstone%7D1p%7Bnstone%7Dppp-3%7Bnstone%7D1%7Bbird%7D1%7Bnstone%7D3-PPP%7Bnstone%7DP1%7Bnstone%7D3--R2%7Bnstone%7D%7Bnstone%7D%7Bnstone%7D3---N1B1P3----QB2P2-----BKNRP1&cols=11&font=Optima&set=auto-alfaerie&shape=vhex&bcolor=FFFFF0&board=201.012.120.&colors=olive+darkkhaki+darkolivegreen&tcolor=000000">
<P>But this is what I described:</P>
<IMG SRC="/play/pbm/drawdiagram.php?code=1prnqb-----2p%7Bnstone%7D1bk----3%7Bnstone%7D%7Bnstone%7Db1n---1%7Bnstone%7D%7Bnstone%7D%7Bnstone%7Dp%7Bnstone%7D%7Bnstone%7D%7Bnstone%7Dr--2%7Bnstone%7D2pp%7Bnstone%7Dpp-3%7Bnstone%7D1%7Bbird%7D1%7Bnstone%7D3-PP%7Bnstone%7DPP2%7Bnstone%7D2--R%7Bnstone%7D%7Bnstone%7D%7Bnstone%7DP%7Bnstone%7D%7Bnstone%7D%7Bnstone%7D1---N1B%7Bnstone%7D%7Bnstone%7D%7Bnstone%7D2----QB1%7Bnstone%7DP2-----BKNRP1&cols=11&font=Optima&set=auto-alfaerie&shape=vhex&bcolor=FFFFF0&board=201.012.120.&colors=olive+darkkhaki+darkolivegreen&tcolor=000000">
<P>Actually, if you include any space that could be reached in two steps but not in one, it would include even more spaces that the Thunderbird could reach. This shows that the idea of a perimeter does not smoothly translate from square boards to hexagonal boards.</P>
<P>Turning to the Pegasus, its moves could all be diagrammed if the first way is what you have in mind for the Thunderbird, and the Pegasus move just extends this out. But if the second way is what you have in mind, there might not be a position on the board from which all Pegasus moves can be diagrammed.</P>
<P>I actually made these diagrams with the problem composer, then switched to the the diagram designer, because the problem composer lets me use Game CODE to clear the board and place pieces on it.</P>