The Equihopper is a fairy piece which was invented by George Leathem
An Equihopper may hop over any unit (friend or enemy) and will land
on the square which is the diametrical opposite of its springboard (hence
the name). When it leaps along Q-lines, all squares between the Equihopper,
the springboard and the destination must be empty (otherwise the leap
is not possible.)
It is depicted as a rotated Queen, and denoted by E.
To illustrate this, consider the following position:
(White Equihopper h2, Black Equihopper h6)
The Equihopper h6 may go to f6 (over g6).
It may not go to b6 (over e6) because
of the g6 (or d6) obstacle. It may capture the wRb2
(over e4). Actually, it gives check to the wK (over f4).
Wh. can answer the check by moving its K, by playing 1. f4-f5
(removing the springboard) or (because this check is along a Q-line),
by playing 1. Rg5/Re3 (blocking the leap). Notice how
these 2 Rook moves give check to the bK !!
Chess algebraists will immediately notice that an Equihopper always
remains on same-color squares (but that's not the whole story). Then
they will ask if an E may play a neutral move by leaping over itself:
it may not!
With non-stop equihoppers, the above position would have both Kings