Further to my last article (published on the 26th March) Harry White has kindly run a computer programme to verify and validate my hypothesis: The 4th-order magic tori are indeed totally covered by sub-magic 2x2 squares.
As Harry White's results gave 7,712 sub-squares for the 880 Frénicle squares it was necessary to determine which tori had a reduced cover of sub-magic squares. After verification I have found that there are two families of the type 2 and type 5 tori. My latest results and totals are given below. It could be that by using observation and manual input I have overlooked something. Your comments are always welcome.
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Please note that the type number of this torus is no longer T4.05.2 but now T4.05.3 |
Conclusion :
Please note that I have published a new article that extends the above findings.
The new table below is a new résumé of the different 4th-order magic tori taking into account the different arrangements of the sub-magic 2x2 squares that cover them.
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