💡📝Graeme Neatham wrote on Mon, Dec 3, 2007 05:39 PM UTC:
Your example piece is a red herring.
My example piece may well be called a herring, red or otherwise, but it illustrates that topological equivalence, though necessary, is not sufficient for game equivalence. That having been said, I agree that for the pieces actually used in Penturanga there is game equivalence between the pentagonal and the hexagonal boards.
... but this is a mathematical problem with a definitive answer.
Exactly! A square has 4 sides, a hexagon has 6 sides, a triangle 3 sides, and a pentagon 5 sides. A board with 6-sided cells is termed hexagonal, so surely it is correct to term a board with 5-sided cells pentagonal?
Your example piece is a red herring.
My example piece may well be called a herring, red or otherwise, but it illustrates that topological equivalence, though necessary, is not sufficient for game equivalence. That having been said, I agree that for the pieces actually used in Penturanga there is game equivalence between the pentagonal and the hexagonal boards.
... but this is a mathematical problem with a definitive answer.
Exactly! A square has 4 sides, a hexagon has 6 sides, a triangle 3 sides, and a pentagon 5 sides. A board with 6-sided cells is termed hexagonal, so surely it is correct to term a board with 5-sided cells pentagonal?
Cheers
Graeme