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. Triangular / King cornered to start is interesting because
  I     ._.  F.i.d.e. / there is only one step out from triangle 50.
 II    ._._.  board   / King has that Rook one-step 50-51.  With board
5-9   ._._._.  of 64  / equilateral triangular in the large, K 50-26
 IV  ._._._._.  cells / is actually a Bishop two-step over cell 37, 
  V ._._._._._.         not a Rook. That is the better logic of using
 VI._._._._._._.        triangles.  Now from more central 26 King is 
  ._._._._._._._.       safer. Three choices to move exist from there,
 ._._._._._._._._.      26-27, 26-38 and 26-40.  More likely he will be 
(Level VIII 50-64)      surrounded by Pawns and pieces there protecting one another mutually.  So, Triangle 26 is ideal standard Castling location, and White's corresponding is 36 for considerable separation. Rook's going to 37, Bunko Leap, in the Castling puts Rook a single step from 51, which is a co-intersection with 50 of the longest Rook ''files.''  For example, Rook 51-64 is 7 steps notionally across 13 equilateral triangles. Thus fixed Castling, Rook towards the corner and King towards the center, helps both of them. King can safely exit his dangerous lock-in at corner with only the one escape by timely Castle. The admonition to Castle Early transposes from F.id.e. squares to triangles in unchanged 64.
For visualization: http://www.chessvariants.org/shape.dir/klinzha/klinzha.html.
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