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Charles Gilman wrote on Fri, Jun 18, 2004 06:41 AM UTC:
```Hippogonal seems a non sequitur to me. Better to describe oblique
(non-radial) directions by their coordinates: thus the Knight, Camel, and
Zebra move along the 2:1, 3:1, and 3:2 obliques respectively. Many others
on the square board are listed in From Ungulates Outwards, which also
gives the formula for duality of moves at 45° to each other. Here are some
reasons to avoid square-board names for hex-specific pieces.
Matching is more 'obvious' to some than to others. In the all-radial
Wellisch Hex Chess, the diagonal piece (which is short-range) is called a
Knight!
Many of my piece names use duality, as this is linked to binding. If both
coordinates are odd, as in the Camel, binding is the same as for the Bishop
- inspiring the names Zemel, Gimel, Namel for leapers in other such
directions. Duality on a hex board is entirely different. Extrapolating
from the Glinsky/McCooey use of 'Knight' would give an unbound 'Camel'
but a 'Giraffe' bound to a third of the board.
It is unwise to ignore the cubic board when dealing with the hex one.
Consider a hex board with cells designated ia1 to ph8. Now consider just
ia1, ja2, jb1, ka3, kb2, kc1, la4, lb3, lc2, ld1 &c.. The diagonals
between those cells are exactly like the orthogonals on a hex board. This
is like the link between just the white squares of a FIDE board and a
board of 7 rows of 2/4/6/8/6/4/2 squares. However the latter transforms
orthogonals to diagonals as well as vv, whereas the cubic-hex
transformation LOSES the original orthogonal. This means that the hex
board does not have the standard diagonal. The diagonal that it does have
transforms from the 2:1:1 oblique, which may explain why Wellisch
considered that direction oblique itself.
Now consider a hex-prism board of 15 8-cell files in triangular formation
a bc def ghij klmno (used for a variant that I will soon be submitting).
The line k1-l2-m3-n4-o5 is plainly a square-board diagonal but, by
rotation, so is a1-c2-f3-j4-o5. The logical move for a Bishop on this
board would be all such diagonals. With such a range of moves a Bishop
could actually reach the whole board (note j4 and n4 both being reachable
from o5), as could a Camel or Zemel similarly defined by the three planes
of square boards. There is no need or reason to include a same-rank (i.e.
same-hex-board) move; after all, the square-board Bishop has none.```

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