Subsets of bimagic 8x8-squares

Sets with essentially different bimagic squares of order 8

Each ess. diff. SQ can be transformed into 192 unique SQ (including the SQ itself) by magic transformations.
Each SQ is written in standard position for ess. diff. magic 8x8-squares.

Amount	Discription of the squares	Download	Sample
841	Centrally symmetric	Data (TXT)
0	Axially symmetric	Proof (PDF)
0	Compact	Proof (PDF)
472	Made of two diagonal Latin squares	Data (TXT)	Sample
448	Non-symmetric but with symmetric main diagonals	Data (TXT)
3567	Complementary invariant - non-symmetric main diagonals which consist of 4 complementary pairs of numbers	Data (TXT)
2424	Complementary invariant - one main diagonal is the complement of the other	Data (TXT)
	There are no further complementary invariant SQ. Total amount: 841 + 3567 + 2424 = 6832

Sets with unique bimagic squares of order 8

Each SQ is written in standard position for unique magic 8x8-squares.
Certain magic properties of special magic squares are not invariant with respect to magic transformations.
For example magic diagonals that are not main diagonals. Therefore sets with unique SQ are necessary.

Amount	Discription of the squares	Download	Sample
29376	Complete	Data (ZIP)
7288	Pandiagonal but not complete	Data (ZIP)
10496	Complete with bimagic semi-diagonals (can be transformed in centrally symmetric squares)	Data (ZIP)
640	Complete with bimagic semi-diagonals made of two Latin squares with Latin main diagonals	Data (TXT)	Sample
256	Pandiagonal with 8 bimagic diagonals	Data (TXT)	Sample
96	Symmetric with 4 semi-magic 4x4-squares	Data (TXT)	Sample
448	Central magic 4x4-square	Data (TXT)	Sample
715	Water retention at least 500 units Maximum water retention: 620	Data (TXT)	Water Retention

Harry White has done similar investigations on our set of bimagic 8x8-squares. See: MultiMagic (External Link)

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