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A chessboard in the form of a honeycomb is an interesting idea, but this
game hardly does it justice. There is potential for pieces from square and
hexagonal boards as well as new combinations. Here are a few directions,
identified by the square of the coprime leap, with the number of adjacent
cells midboard in brackets. Excuse the punning name suggestions, which
follow in the vein of Sexton for the 2:1:1 on a cubic board.
1(8) orthogonal, hexagonlly in one layer or squarely at right angles to
it.
2(12) diagonal, as the square Bishop, equal distances in both kinds of
orthogonal direction; not colourbound and always changes layer.
3(6) as the hex piece commonly called Bishop, bound to both colour and
layer; same length as 1:1:1 on a cubic board, for which I favour Viceroy
for the leaper and Unicorn for the linepiece, but with no possible
confusion I suggest them for this direction too.
4(12) equal numbers of cells as above and on the square orthogonal; same
length as Dabbaba, so the leaper might be called Rumbaba and the linepiece
Rumbabante or Rumbarider.
5(24) as square Knight/-rider, 2 cells in one kind of orthogonal direction
and 1 in the other.
7(24) as the hex piece commonly called Knight, OR 2 cells on the square
orthogonal and 1 as a 'Unicorn'; leaper could be termed Sennight
(meaning seven-day week).
8(24) 1 cell on the square orthogonal and 1 as a 'Sennight'; same length
as Alfil, so the leaper might be called a Heffalump.
10(24) as Camel/-rider, 3 cells in one kind of orthogonal direction and 1
in the other.
11(24) 2 cells on the square orthogonal and 1 as a 'Sennight'; same
length as 3:1:1 on a cubic board, but with no possible confusion I suggest
Elf for both.
13(48) as Zebra/-rider, 3 cells in one kind of orthogonal direction and 2
in the other, OR 2 as a 'Unicorn' and 1 in an orthogonal direction at
right angles to it.
14(24) 2 cells as a 'Unicorn' and 1 in a diagonal direction at right
angles to it; same length as 3:2:1 on a cubic board, but with no possible
confusion I suggest Fortnight for both.