The Magic Encyclopedia ™ DataBase

trimagic squares order 12
(by Aale de Winkel / Walter Trump)

<Walter Trump> sent us the first order 12 trimagic square ever found, from this square with symmetric diagonal permutation 12!!/2 = 23040 other trimagic squares can be obtained. The one with the smallest permutation along the main diagonal I named the "Least Diagonal Representative", any derived trimagic square will have a higher permutation of the same numbers along the main diagonal. Thus defined the squares are best listed by the "Least Diagonal Representative" (LDR) and derive a particular square within the thus defined "family" as LDR_{_[perm]} (note: _[..] as defined by the hypercube language) This gives the square Walter Trump found as LDR_0_{_[00 06 02 10 04 08 03 07 01 09 05 11]} with LDR_0 its corresponding "Least Diagonal Representative". The feature Walter aimed at was the lineup in the squares frist row.
The excell trimagic order 12 spreadsheet gives access to all related trimagic squares, just mention the given permutation will be enough to alert attention to a particular square within these 23040 squares
Note: this is a recent development, more LDR's will get listed as they come available to me!

trimagic squares order 12

Walter Trump square LDR_0_[00 06 02 10 04 08 03 07 01 09 05 11] 001 022 033 041 062 066 079 083 104 112 123 144 009 119 045 115 107 093 052 038 030 100 026 136 075 141 035 048 057 014 131 088 097 110 004 070 074 008 106 049 012 043 102 133 096 039 137 071 140 101 124 042 060 037 108 085 103 021 044 005 122 076 142 086 067 126 019 078 059 003 069 023 055 027 095 135 130 089 056 015 010 050 118 090 132 117 068 091 011 099 046 134 054 077 028 013 073 064 002 121 109 032 113 036 024 143 081 072 058 098 084 116 138 016 129 007 029 061 047 087 080 034 105 006 092 127 018 053 139 040 111 065 051 063 031 020 025 128 017 120 125 114 082 094

Least Diagonal Representative LDR_0 001 104 033 079 062 123 022 083 066 112 041 144 073 024 002 113 109 081 064 036 032 143 121 072 075 097 035 131 057 004 141 088 014 110 048 070 055 010 095 056 130 118 027 015 089 050 135 090 140 103 124 108 060 044 101 085 037 021 042 005 080 139 105 018 092 111 034 053 127 040 006 065 009 030 045 052 107 026 119 038 093 100 115 136 132 054 068 046 011 028 117 134 099 077 091 013 122 059 142 019 067 069 076 078 126 003 086 023 058 029 084 129 138 047 098 007 016 061 116 087 074 096 106 102 012 137 008 133 043 039 049 071 051 125 031 017 025 082 063 120 128 114 020 094