[Magictour] Re: 12x12

What is the meaning of this term "semi-regular"?
Have I not been paying attention and missed the definition somewhere? =
It's not a term I recognise.

see http://www.ktn.freeuk.com/mg.htm#(3)
last sentences before #(4) "Method of Braids"


"Hoist with my own petard" it seems.
In view of the new discoveries, in particular tours 14e, 00n, 00o,
I doubt if this terminology is any longer of much use,
if it ever was. I will be removing it.

Instead of making a search based on quartes or 4-strand braids I would =
suggest that, looking at the structure of Mr Kumar's diagonal magic =
tours a search should be based on two-strand braids, or what Murray =
called "contiguous contraparallel chains".

If you follow the two chains 1 - 36 and 73 - 108 you will see that they =
fill alternate half-blocks (dominos) which all add to 109. Similarly 37 =
- 72 and 109 - 144 form half-bocks adding to 181. These in pairs add to =
290 which is a third of the magic constant.

If the chains are taken the other way round 1 - 36 with 37 - 72 and 73 - =
108 with 109 - 144 they also almost form a complete domino pattern, =
though not contiguous everywhere.

GPJ




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Received on Thu Dec 04 14:24:18 2001