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Chess Geometry[Subject Thread] [Add Response]
Charles Gilman wrote on Wed, Feb 5, 2014 07:24 AM UTC:
Ben Reiniger is quite correct, and what he describes is the basis of the dualities between hex or Tetrahedral (alias Xyrixa) and cubic pieces in pages 14 and 18 of Man and Beast. Taking out one Bishop binding of a cubic board converts a cubic piece whose coordinates are 2m Wazir steps at right angles to n Ferz ones into a Tetrahedral/Xyrixa piece whose coordinates are n Wazir steps at right angles to m Ferz ones, and an m+n:m:n leaper into a piece moving along a hex plane. The first gives dualities such as Lecturer/Elf, Effarig/Fencer, and Nurturer/Underscore while the seciond gives dualities such as Fortnight/Sennight, Sustainer/Student, and Votary/Overscore. Ferz/Wazir and Sexton/Viceroy fit both.