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Christine Bagley-Jones wrote on Fri, Jun 15, 2012 04:47 AM UTC:
Laugh, ok, here are some more.

'Operational Chess' by Andy Thomas, January 2006. 
Piece called 'General', leaps 3 squares away, all directions.
Thus, it is a 0,3 and 3,3 leaper, and also can move like the 3,1 Camel and the 3,2 Zebra.

'Scirocco' by Adrian King, 1999, piece called 'Frog'.
Leaps as a (0,3) or (3,3) leaper, plus can move 1 square all directions.

G.P.Jelliss gives these names and movements.
'Frog' {1,1}+{0,3}, 'Toad' {0,2}+{0,3} and 'Newt' {2,2}+{0,3}
Also 'Threeleaper' {0,3}, and 'Tripper' {3,3}.
The 'Threeleaper' and 'Tripper' are in my game 'Sky', under those names.
You can see the 'frog' {1,1}+{0,3} in 'Presiding Chess' by Tucker Kao, 2003.
In 'Quangtrung Chess' by Vu Q, 2002, piece 'Voi' moves like above 'Newt'.

Chess with Different Armies has the 'Half-Duck', steps 1 space diagonally, or jumps 2 or 3 orthogonally.

'The Travelers' by Roberto Lavieri, 2006.
Piece called 'Trey', has non-capture and capture moves, as follows.
Non-capturing: slides 1-3 squares orthogonally or diagonally.
Capturing: can leap 3 squares, 0,3 and 3,3, only to capture.

In 'Jetan', (Martian Chess) by Edgar Rice Burroughs, piece called 'Flier'.
The Flier moves three squares diagonally or in a combination of these diagonal directions. It may jump over intervening pieces.

I do not know of a piece that is a pure 0,3 and 3,3 leaper.
Not saying there isn't one, with so many chess variants and pieces, 
just saying i have not seen it, as far as i can recall.

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