The tiling (6) and (7)
can be decomposed by two pair-symmetry tiling.
Thus, an element 
of (6)
is calculated with the corresponding elements 
of (1) by
An element 
of (7)
is calculated with the corresponding elements of (1)
where R is rotation operator which makes the operand rotate 
around an arbitrary element.
We call such fundamental tiling pattern 
``ideal tiling of the order N'' which
satisfies the maximal symmetry.
Through this considerations, we could expect the following conjecture:
For example, if the order N can be decomposed by the divisors a,b,c,d, thus
the ideal tiling of order N is given by
using decomposed ideal tiling of the divisors' orders a,b,c,d,
where 
is an operator of symmetrical change.
