01,20,47,62 28,09,54,39 45,64,03,18 56,37,26,11 48,61,02,19 53,40,27,10 04,17,46,63 25,12,55,38 29,16,51,34 08,21,42,59 49,36,31,14 44,57,06,23 52,33,30,15 41,60,07,22 32,13,50,35 05,24,43,58 1. Awani Kumar 2006 4 cub4k01, 1. Awani Kumar 2006 , 1 20 ... 58 0 64 not a path-cube first entry in : (1,1,1) not associated (0 errors) 0 out of 4 main triagonals are wrong 24 out of 24 main diagonals are wrong 16 64 out of 64 k*k*k block-corners are wrong 80 192 out of 192 1*k*k block-corners are wrong sublattice 2 : 8 faults 64 out of 64 pantriagonals are noncomplete 001: 0 0 3 48 0 2 0 2 0 0 002: 1 24 0 0 1 1 0 1 1 1 011: 6 96 6 80 6 6 6 6 2 6 012: 5 80 6 96 2 4 0 4 4 4 022: 1 24 0 0 1 1 1 1 0 1 111: 4 32 4 32 0 0 0 0 4 4 112: 6 96 6 80 6 6 6 6 2 6 122: 3 48 2 32 2 2 0 2 2 2 222: 0 8 0 0 0 0 0 0 0 0 pan(2) ratio = 584/992 = 0.588710 panmagic ratio = 80/208 = 0.384615 magic ratio = 52/76 = 0.684211 latin ratio: 80/144 = 0.555556 contains 1 latin cube 01,20,47,62 28,37,54,11 45,64,03,18 56,09,26,39 48,61,02,19 53,12,27,38 04,17,46,63 25,40,55,10 29,16,51,34 44,21,06,59 49,36,31,14 08,57,42,23 52,33,30,15 05,60,43,22 32,13,50,35 41,24,07,58 2. Awani Kumar 2006 4 cub4k02, 2. Awani Kumar 2006 , 1 20 ... 58 0 64 not a path-cube first entry in : (1,1,1) not associated (0 errors) 4 out of 4 main triagonals are wrong 24 out of 24 main diagonals are wrong 32 64 out of 64 k*k*k block-corners are wrong 112 192 out of 192 1*k*k block-corners are wrong sublattice 2 : 8 faults 64 out of 64 pantriagonals are noncomplete 001: 0 0 3 40 0 2 0 2 0 0 002: 1 24 0 0 1 1 0 1 1 1 011: 6 96 6 96 6 6 6 6 6 6 012: 5 80 6 96 2 4 1 4 4 4 022: 1 24 0 0 1 1 1 1 1 1 111: 4 64 4 64 0 0 4 4 4 4 112: 6 96 6 88 6 6 6 6 6 6 122: 3 48 2 24 2 2 0 2 2 2 222: 0 8 0 0 0 0 0 0 0 0 pan(2) ratio = 552/992 = 0.556452 panmagic ratio = 48/208 = 0.230769 magic ratio = 48/76 = 0.631579 latin ratio: 80/144 = 0.555556 contains 1 latin cube 01,24,47,58 42,63,08,17 55,02,25,48 32,41,50,07 46,59,04,21 05,20,43,62 28,45,54,03 51,06,29,44 23,34,57,16 64,09,18,39 33,56,15,26 10,31,40,49 60,13,22,35 19,38,61,12 14,27,36,53 37,52,11,30 3. Guenter Stertenbrink 2003 4 cub4k03, 3. Guenter Stertenbrink 2003 , 1 24 ... 30 0 64 not a path-cube first entry in : (1,1,1) not associated (0 errors) 2 out of 4 main triagonals are wrong 24 out of 24 main diagonals are wrong 16 64 out of 64 k*k*k block-corners are wrong 128 192 out of 192 1*k*k block-corners are wrong sublattice 2 : 8 faults 64 out of 64 pantriagonals are noncomplete 001: 0 0 3 32 0 0 0 0 0 0 002: 1 24 0 0 1 1 1 1 1 1 011: 6 96 6 96 6 6 6 6 6 6 012: 6 80 5 80 0 0 2 4 5 6 022: 1 24 0 0 1 1 1 1 1 1 111: 4 48 4 64 0 0 0 4 4 4 112: 6 96 6 96 6 6 6 6 6 6 122: 2 32 3 40 0 0 2 2 0 0 222: 0 8 0 0 0 0 0 0 0 0 pan(2) ratio = 584/992 = 0.588710 panmagic ratio = 64/208 = 0.307692 magic ratio = 50/76 = 0.657895 latin ratio: 144/144 = 1.000000 contains 3 orthogonal latin cubes 01,46,23,60 42,05,64,19 55,28,33,14 32,51,10,37 56,27,02,45 31,52,41,06 34,13,24,59 09,38,63,20 47,04,57,22 08,43,18,61 25,54,15,36 50,29,40,11 26,53,48,03 49,30,07,44 16,35,58,21 39,12,17,62 4. Guenter Stertenbrink 2003 4 cub4k04, 4. Guenter Stertenbrink 2003 , 1 46 ... 62 0 64 not a path-cube first entry in : (1,1,1) not associated (0 errors) 2 out of 4 main triagonals are wrong 24 out of 24 main diagonals are wrong 16 64 out of 64 k*k*k block-corners are wrong 128 192 out of 192 1*k*k block-corners are wrong sublattice 2 : 8 faults 64 out of 64 pantriagonals are noncomplete 001: 0 0 3 32 0 0 0 0 0 0 002: 1 24 0 0 1 1 1 1 1 1 011: 6 96 6 96 6 6 6 6 6 6 012: 6 80 6 88 0 0 2 4 6 6 022: 1 24 0 0 1 1 1 1 1 1 111: 4 48 4 64 0 0 0 4 4 4 112: 6 96 6 96 6 6 6 6 6 6 122: 2 32 3 32 0 0 2 2 0 0 222: 0 8 0 0 0 0 0 0 0 0 pan(2) ratio = 584/992 = 0.588710 panmagic ratio = 64/208 = 0.307692 magic ratio = 50/76 = 0.657895 latin ratio: 144/144 = 1.000000 contains 3 orthogonal latin cubes 03,18,45,64 54,11,28,37 47,62,01,20 26,39,56,09 46,63,04,17 27,38,53,12 02,19,48,61 55,10,25,40 31,14,49,36 06,59,44,21 51,34,29,16 42,23,08,57 50,35,32,13 43,22,05,60 30,15,52,33 07,58,41,24 5. Awani Kumar 2006 4 cub4k05, 5. Awani Kumar 2006 , 3 18 ... 24 0 64 not a path-cube first entry in : (1,3,3) not associated (0 errors) 4 out of 4 main triagonals are wrong 24 out of 24 main diagonals are wrong 32 64 out of 64 k*k*k block-corners are wrong 112 192 out of 192 1*k*k block-corners are wrong sublattice 2 : 8 faults 64 out of 64 pantriagonals are noncomplete 001: 0 0 3 40 0 2 0 2 0 0 002: 1 24 0 0 1 1 0 1 1 1 011: 6 96 6 96 6 6 6 6 6 6 012: 5 80 6 96 2 4 1 4 4 4 022: 1 24 0 0 1 1 1 1 1 1 111: 4 64 4 64 0 0 4 4 4 4 112: 6 96 6 88 6 6 6 6 6 6 122: 3 48 2 24 2 2 0 2 2 2 222: 0 8 0 0 0 0 0 0 0 0 pan(2) ratio = 552/992 = 0.556452 panmagic ratio = 48/208 = 0.230769 magic ratio = 48/76 = 0.631579 latin ratio: 80/144 = 0.555556 contains 1 latin cube 03,26,47,54 18,11,62,39 45,56,01,28 64,37,20,09 46,55,02,27 63,38,19,10 04,25,48,53 17,12,61,40 31,06,51,42 14,23,34,59 49,44,29,08 36,57,16,21 50,43,30,07 35,58,15,22 32,05,52,41 13,24,33,60 6. Awani Kumar 2006 4 cub4k06, 6. Awani Kumar 2006 , 3 26 ... 60 0 64 not a path-cube first entry in : (1,3,3) not associated (0 errors) 0 out of 4 main triagonals are wrong 24 out of 24 main diagonals are wrong 16 64 out of 64 k*k*k block-corners are wrong 80 192 out of 192 1*k*k block-corners are wrong sublattice 2 : 8 faults 64 out of 64 pantriagonals are noncomplete 001: 0 0 3 48 0 2 0 2 0 0 002: 1 24 0 0 1 1 0 1 1 1 011: 6 96 6 80 6 6 6 6 2 6 012: 5 80 6 96 2 4 0 4 4 4 022: 1 24 0 0 1 1 1 1 0 1 111: 4 32 4 32 0 0 0 0 4 4 112: 6 96 6 80 6 6 6 6 2 6 122: 3 48 2 32 2 2 0 2 2 2 222: 0 8 0 0 0 0 0 0 0 0 pan(2) ratio = 584/992 = 0.588710 panmagic ratio = 80/208 = 0.384615 magic ratio = 52/76 = 0.684211 latin ratio: 80/144 = 0.555556 contains 1 latin cube 03,46,31,50 26,55,06,43 47,02,51,30 54,27,42,07 64,17,36,13 37,12,57,24 20,61,16,33 09,40,21,60 45,04,49,32 56,25,44,05 01,48,29,52 28,53,08,41 18,63,14,35 11,38,23,58 62,19,34,15 39,10,59,22 7. Awani Kumar 2007 4 cub4k07, 7. Awani Kumar 2007 , 3 46 ... 22 0 64 not a path-cube first entry in : (3,3,1) not associated (0 errors) 4 out of 4 main triagonals are wrong 24 out of 24 main diagonals are wrong 16 64 out of 64 k*k*k block-corners are wrong 80 192 out of 192 1*k*k block-corners are wrong sublattice 2 : 8 faults 64 out of 64 pantriagonals are noncomplete 001: 0 0 3 48 0 2 0 2 0 0 002: 1 24 0 0 1 1 0 1 1 1 011: 6 96 6 80 6 6 6 6 2 6 012: 5 80 6 96 2 4 0 4 4 4 022: 1 24 0 0 1 1 1 1 0 1 111: 4 32 4 32 0 0 0 0 4 4 112: 6 96 6 80 6 6 6 6 2 6 122: 3 48 2 32 2 2 0 2 2 2 222: 0 8 0 0 0 0 0 0 0 0 pan(2) ratio = 584/992 = 0.588710 panmagic ratio = 80/208 = 0.384615 magic ratio = 48/76 = 0.631579 latin ratio: 80/144 = 0.555556 contains 1 latin cube 03,46,31,50 54,27,06,43 47,02,51,30 26,55,42,07 64,17,36,13 37,12,21,60 20,61,16,33 09,40,57,24 45,04,49,32 28,53,44,05 01,48,29,52 56,25,08,41 18,63,14,35 11,38,59,22 62,19,34,15 39,10,23,58 8. Awani Kumar 2007 4 cub4k08, 8. Awani Kumar 2007 , 3 46 ... 58 0 64 not a path-cube first entry in : (3,3,1) not associated (0 errors) 4 out of 4 main triagonals are wrong 24 out of 24 main diagonals are wrong 32 64 out of 64 k*k*k block-corners are wrong 112 192 out of 192 1*k*k block-corners are wrong sublattice 2 : 8 faults 64 out of 64 pantriagonals are noncomplete 001: 0 0 3 40 0 2 0 2 0 0 002: 1 24 0 0 1 1 0 1 1 1 011: 6 96 6 96 6 6 6 6 6 6 012: 5 80 6 96 2 4 2 4 4 4 022: 1 24 0 0 1 1 1 1 1 1 111: 4 64 4 64 0 0 4 4 4 4 112: 6 96 6 88 6 6 6 6 6 6 122: 3 48 2 24 2 2 0 2 2 2 222: 0 8 0 0 0 0 0 0 0 0 pan(2) ratio = 552/992 = 0.556452 panmagic ratio = 48/208 = 0.230769 magic ratio = 48/76 = 0.631579 latin ratio: 80/144 = 0.555556 contains 1 latin cube 03,46,63,18 48,01,20,61 29,52,33,16 50,31,14,35 58,23,06,43 21,60,41,08 40,09,28,53 11,38,55,26 47,02,19,62 04,45,64,17 49,32,13,36 30,51,34,15 22,59,42,07 57,24,05,44 12,37,56,25 39,10,27,54 9. Awani Kumar 2007 4 cub4k09, 9. Awani Kumar 2007 , 3 46 ... 54 0 64 not a path-cube first entry in : (1,2,2) not associated (0 errors) 0 out of 4 main triagonals are wrong 24 out of 24 main diagonals are wrong 16 64 out of 64 k*k*k block-corners are wrong 96 192 out of 192 1*k*k block-corners are wrong sublattice 2 : 8 faults 64 out of 64 pantriagonals are noncomplete 001: 0 0 2 32 0 2 0 2 0 0 002: 1 24 0 0 1 1 0 1 1 1 011: 6 96 6 80 6 6 6 6 4 6 012: 5 80 5 80 2 4 0 4 4 6 022: 1 24 0 0 1 1 1 1 1 1 111: 4 48 4 64 0 0 0 0 4 4 112: 6 96 6 80 6 6 6 6 4 6 122: 2 32 3 48 2 2 0 2 0 0 222: 0 8 0 0 0 0 0 0 0 0 pan(2) ratio = 584/992 = 0.588710 panmagic ratio = 64/208 = 0.307692 magic ratio = 52/76 = 0.684211 latin ratio: 80/144 = 0.555556 contains 1 latin cube 03,46,63,18 48,17,04,61 29,52,33,16 50,15,30,35 58,23,06,43 05,60,41,24 40,09,28,53 27,38,55,10 47,02,19,62 20,45,64,01 49,32,13,36 14,51,34,31 22,59,42,07 57,08,21,44 12,37,56,25 39,26,11,54 10. Awani Kumar 2007 4 cub4k10, 10. Awani Kumar 2007 , 3 46 ... 54 0 64 not a path-cube first entry in : (3,2,4) not associated (0 errors) 0 out of 4 main triagonals are wrong 24 out of 24 main diagonals are wrong 16 64 out of 64 k*k*k block-corners are wrong 128 192 out of 192 1*k*k block-corners are wrong sublattice 2 : 8 faults 64 out of 64 pantriagonals are noncomplete 001: 0 0 3 32 0 2 0 2 0 0 002: 1 24 0 0 1 1 0 1 1 1 011: 6 96 6 96 6 6 6 6 6 6 012: 6 80 6 88 2 4 0 4 6 6 022: 1 24 0 0 1 1 1 1 1 1 111: 4 48 4 64 0 0 0 0 4 4 112: 6 96 6 96 6 6 6 6 6 6 122: 2 32 3 32 2 2 0 2 0 0 222: 0 8 0 0 0 0 0 0 0 0 pan(2) ratio = 584/992 = 0.588710 panmagic ratio = 64/208 = 0.307692 magic ratio = 52/76 = 0.684211 latin ratio: 80/144 = 0.555556 contains 1 latin cube 03,46,63,18 64,01,20,45 29,52,33,16 34,31,14,51 58,23,06,43 21,44,57,08 40,09,28,53 11,54,39,26 47,02,19,62 04,61,48,17 49,32,13,36 30,35,50,15 22,59,42,07 41,24,05,60 12,37,56,25 55,10,27,38 11. Awani Kumar 2007 4 cub4k11, 11. Awani Kumar 2007 , 3 46 ... 38 0 64 not a path-cube first entry in : (1,2,2) not associated (0 errors) 4 out of 4 main triagonals are wrong 24 out of 24 main diagonals are wrong 16 64 out of 64 k*k*k block-corners are wrong 128 192 out of 192 1*k*k block-corners are wrong sublattice 2 : 8 faults 64 out of 64 pantriagonals are noncomplete 001: 0 0 3 32 0 2 0 2 0 0 002: 1 24 0 0 1 1 0 1 1 1 011: 6 96 6 96 6 6 6 6 6 6 012: 6 80 6 88 2 4 0 4 6 6 022: 1 24 0 0 1 1 1 1 1 1 111: 4 48 4 64 0 0 0 0 4 4 112: 6 96 6 96 6 6 6 6 6 6 122: 2 32 3 32 2 2 0 2 0 0 222: 0 8 0 0 0 0 0 0 0 0 pan(2) ratio = 584/992 = 0.588710 panmagic ratio = 64/208 = 0.307692 magic ratio = 48/76 = 0.631579 latin ratio: 80/144 = 0.555556 contains 1 latin cube 03,46,63,18 64,17,04,45 29,52,33,16 34,15,30,51 58,23,06,43 05,44,57,24 40,09,28,53 27,54,39,10 47,02,19,62 20,61,48,01 49,32,13,36 14,35,50,31 22,59,42,07 41,08,21,60 12,37,56,25 55,26,11,38 12. Awani Kumar 2007 4 cub4k12, 12. Awani Kumar 2007 , 3 46 ... 38 0 64 not a path-cube first entry in : (3,2,4) not associated (0 errors) 4 out of 4 main triagonals are wrong 24 out of 24 main diagonals are wrong 16 64 out of 64 k*k*k block-corners are wrong 96 192 out of 192 1*k*k block-corners are wrong sublattice 2 : 8 faults 64 out of 64 pantriagonals are noncomplete 001: 0 0 3 48 0 2 0 2 0 0 002: 1 24 0 0 1 1 0 1 1 1 011: 6 96 6 80 6 6 6 6 4 6 012: 5 80 5 80 2 4 0 4 4 6 022: 1 24 0 0 1 1 1 1 1 1 111: 4 48 4 64 0 0 0 0 4 4 112: 6 96 6 80 6 6 6 6 4 6 122: 2 32 2 32 2 2 0 2 0 0 222: 0 8 0 0 0 0 0 0 0 0 pan(2) ratio = 584/992 = 0.588710 panmagic ratio = 64/208 = 0.307692 magic ratio = 48/76 = 0.631579 latin ratio: 80/144 = 0.555556 contains 1 latin cube 03,48,29,50 46,01,52,31 63,20,33,14 18,61,16,35 58,21,12,39 23,60,37,10 42,05,28,55 07,44,53,26 47,04,49,30 02,45,32,51 19,64,13,34 62,17,36,15 22,57,40,11 59,24,09,38 06,41,56,27 43,08,25,54 13. Awani Kumar 2007 4 cub4k13, 13. Awani Kumar 2007 , 3 48 ... 54 0 64 not a path-cube first entry in : (1,2,2) not associated (0 errors) 2 out of 4 main triagonals are wrong 24 out of 24 main diagonals are wrong 16 64 out of 64 k*k*k block-corners are wrong 88 192 out of 192 1*k*k block-corners are wrong sublattice 2 : 8 faults 64 out of 64 pantriagonals are noncomplete 001: 0 0 3 40 0 2 0 2 0 0 002: 1 24 0 0 1 1 1 1 1 1 011: 6 96 6 72 6 6 6 6 6 6 012: 6 80 6 88 2 4 2 4 6 6 022: 1 24 0 0 1 1 1 1 1 1 111: 4 48 4 64 0 0 0 0 4 4 112: 6 96 6 88 6 6 6 6 6 6 122: 3 40 3 48 2 2 2 2 0 0 222: 0 8 0 0 0 0 0 0 0 0 pan(2) ratio = 576/992 = 0.580645 panmagic ratio = 64/208 = 0.307692 magic ratio = 50/76 = 0.657895 latin ratio: 80/144 = 0.555556 contains 1 latin cube 03,48,53,26 44,07,30,49 21,58,35,16 62,17,12,39 54,25,36,15 29,50,11,40 04,47,22,57 43,08,61,18 45,02,27,56 06,41,52,31 59,24,13,34 20,63,38,09 28,55,14,33 51,32,37,10 46,01,60,23 05,42,19,64 14. Guenter Stertenbrink 2003 4 cub4k14, 14. Guenter Stertenbrink 2003 , 3 48 ... 64 0 64 not a path-cube first entry in : (4,3,2) not associated (0 errors) 2 out of 4 main triagonals are wrong 24 out of 24 main diagonals are wrong 16 64 out of 64 k*k*k block-corners are wrong 128 192 out of 192 1*k*k block-corners are wrong sublattice 2 : 8 faults 64 out of 64 pantriagonals are noncomplete 001: 0 0 3 32 0 0 0 0 0 0 002: 1 24 0 0 1 1 1 1 1 1 011: 6 96 6 96 6 6 6 6 6 6 012: 6 80 6 88 0 0 2 4 6 6 022: 1 24 0 0 1 1 1 1 1 1 111: 4 48 4 64 0 0 0 4 4 4 112: 6 96 6 96 6 6 6 6 6 6 122: 2 32 3 32 0 0 2 2 0 0 222: 0 8 0 0 0 0 0 0 0 0 pan(2) ratio = 584/992 = 0.588710 panmagic ratio = 64/208 = 0.307692 magic ratio = 50/76 = 0.657895 latin ratio: 144/144 = 1.000000 contains 3 orthogonal latin cubes 05,26,63,36 50,45,12,23 31,04,37,58 44,55,18,13 64,35,06,25 11,24,49,46 38,57,32,03 17,14,43,56 27,08,33,62 48,51,22,09 01,30,59,40 54,41,16,19 34,61,28,07 21,10,47,52 60,39,02,29 15,20,53,42 15. Guenter Stertenbrink 2003 4 cub4k15, 15. Guenter Stertenbrink 2003 , 5 26 ... 42 0 64 not a path-cube first entry in : (3,3,1) not associated (0 errors) 0 out of 4 main triagonals are wrong 24 out of 24 main diagonals are wrong 24 64 out of 64 k*k*k block-corners are wrong 112 192 out of 192 1*k*k block-corners are wrong sublattice 2 : 8 faults 64 out of 64 pantriagonals are noncomplete 001: 0 0 2 32 0 0 0 0 0 0 002: 1 24 0 0 1 1 1 1 1 1 011: 6 96 6 80 6 6 6 6 6 6 012: 4 64 6 96 0 0 2 4 2 4 022: 1 24 0 0 1 1 1 1 1 1 111: 0 0 4 64 0 0 0 4 0 4 112: 6 96 6 80 6 6 6 6 6 6 122: 3 48 2 32 0 0 2 2 2 2 222: 0 8 0 0 0 0 0 0 0 0 pan(2) ratio = 632/992 = 0.637097 panmagic ratio = 112/208 = 0.538462 magic ratio = 52/76 = 0.684211 latin ratio: 144/144 = 1.000000 contains 3 orthogonal latin cubes 05,32,59,34 18,11,48,53 63,38,01,28 44,49,22,15 58,35,08,29 45,56,19,10 04,25,62,39 23,14,41,52 31,06,33,60 12,17,54,47 37,64,27,02 50,43,16,21 36,57,30,07 55,46,09,20 26,03,40,61 13,24,51,42 16. Guenter Stertenbrink 2003 4 cub4k16, 16. Guenter Stertenbrink 2003 , 5 32 ... 42 0 64 not a path-cube first entry in : (1,3,3) not associated (0 errors) 0 out of 4 main triagonals are wrong 24 out of 24 main diagonals are wrong 24 64 out of 64 k*k*k block-corners are wrong 128 192 out of 192 1*k*k block-corners are wrong sublattice 2 : 8 faults 64 out of 64 pantriagonals are noncomplete 001: 0 0 3 48 0 0 0 0 0 0 002: 1 24 0 0 1 1 1 1 0 1 011: 6 96 6 96 6 6 6 6 6 6 012: 3 48 5 80 0 0 2 4 2 4 022: 1 24 0 0 1 1 1 1 1 1 111: 4 32 4 32 0 0 0 4 4 4 112: 6 96 4 64 6 6 6 6 6 6 122: 2 32 2 32 0 0 2 2 0 2 222: 0 8 0 0 0 0 0 0 0 0 pan(2) ratio = 632/992 = 0.637097 panmagic ratio = 80/208 = 0.384615 magic ratio = 52/76 = 0.684211 latin ratio: 144/144 = 1.000000 contains 3 orthogonal latin cubes 05,42,19,64 46,01,60,23 51,32,37,10 28,55,14,33 52,31,06,41 27,56,45,02 38,09,20,63 13,34,59,24 43,08,61,18 04,47,22,57 29,50,11,40 54,25,36,15 30,49,44,07 53,26,03,48 12,39,62,17 35,16,21,58 17. Guenter Stertenbrink 2003 4 cub4k17, 17. Guenter Stertenbrink 2003 , 5 42 ... 58 0 64 not a path-cube first entry in : (1,2,2) not associated (0 errors) 2 out of 4 main triagonals are wrong 24 out of 24 main diagonals are wrong 16 64 out of 64 k*k*k block-corners are wrong 128 192 out of 192 1*k*k block-corners are wrong sublattice 2 : 8 faults 64 out of 64 pantriagonals are noncomplete 001: 0 0 3 32 0 0 0 0 0 0 002: 1 24 0 0 1 1 1 1 1 1 011: 6 96 6 96 6 6 6 6 6 6 012: 6 80 6 88 0 0 2 4 6 6 022: 1 24 0 0 1 1 1 1 1 1 111: 4 48 4 64 0 0 0 4 4 4 112: 6 96 6 96 6 6 6 6 6 6 122: 2 32 3 32 0 0 2 2 0 0 222: 0 8 0 0 0 0 0 0 0 0 pan(2) ratio = 584/992 = 0.588710 panmagic ratio = 64/208 = 0.307692 magic ratio = 50/76 = 0.657895 latin ratio: 144/144 = 1.000000 contains 3 orthogonal latin cubes 07,24,41,58 50,13,32,35 43,60,05,22 30,33,52,15 42,57,08,23 31,36,49,14 06,21,44,59 51,16,29,34 55,40,25,10 46,17,04,63 27,12,53,38 02,61,48,19 26,09,56,39 03,64,45,18 54,37,28,11 47,20,01,62 18. Awani Kumar 2007 4 cub4k18, 18. Awani Kumar 2007 , 7 24 ... 62 0 64 not a path-cube first entry in : (4,4,3) not associated (0 errors) 4 out of 4 main triagonals are wrong 24 out of 24 main diagonals are wrong 32 64 out of 64 k*k*k block-corners are wrong 112 192 out of 192 1*k*k block-corners are wrong sublattice 2 : 8 faults 64 out of 64 pantriagonals are noncomplete 001: 0 0 3 40 0 2 0 2 0 0 002: 1 24 0 0 1 1 0 1 1 1 011: 6 96 6 96 6 6 6 6 6 6 012: 5 80 6 96 2 4 2 4 3 4 022: 1 24 0 0 1 1 1 1 1 1 111: 4 64 4 64 0 0 4 4 4 4 112: 6 96 6 88 6 6 6 6 6 6 122: 3 48 2 24 2 2 0 2 2 2 222: 0 8 0 0 0 0 0 0 0 0 pan(2) ratio = 552/992 = 0.556452 panmagic ratio = 48/208 = 0.230769 magic ratio = 48/76 = 0.631579 latin ratio: 80/144 = 0.555556 contains 1 latin cube 07,42,55,26 50,31,46,03 43,06,27,54 30,51,02,47 58,23,10,39 35,14,63,18 22,59,38,11 15,34,19,62 41,08,25,56 32,49,04,45 05,44,53,28 52,29,48,01 24,57,40,09 13,36,17,64 60,21,12,37 33,16,61,20 19. Awani Kumar 2006 4 cub4k19, 19. Awani Kumar 2006 , 7 42 ... 20 0 64 not a path-cube first entry in : (3,4,4) not associated (0 errors) 4 out of 4 main triagonals are wrong 24 out of 24 main diagonals are wrong 32 64 out of 64 k*k*k block-corners are wrong 112 192 out of 192 1*k*k block-corners are wrong sublattice 2 : 8 faults 64 out of 64 pantriagonals are noncomplete 001: 0 0 3 40 0 2 0 2 0 0 002: 1 24 0 0 1 1 0 1 1 1 011: 6 96 6 96 6 6 6 6 6 6 012: 5 80 6 96 2 4 2 4 4 4 022: 1 24 0 0 1 1 1 1 1 1 111: 4 64 4 64 0 0 4 4 4 4 112: 6 96 6 88 6 6 6 6 6 6 122: 3 48 2 24 2 2 0 2 2 2 222: 0 8 0 0 0 0 0 0 0 0 pan(2) ratio = 552/992 = 0.556452 panmagic ratio = 48/208 = 0.230769 magic ratio = 48/76 = 0.631579 latin ratio: 80/144 = 0.555556 contains 1 latin cube 11,34,55,30 40,29,12,49 21,64,41,04 58,03,22,47 54,31,10,35 09,52,37,32 44,01,24,61 23,46,59,02 39,14,27,50 28,33,56,13 57,20,05,48 06,63,42,19 26,51,38,15 53,16,25,36 08,45,60,17 43,18,07,62 20. Awani Kumar 2007 4 cub4k20, 20. Awani Kumar 2007 , 11 34 ... 62 0 64 not a path-cube first entry in : (2,3,2) not associated (0 errors) 0 out of 4 main triagonals are wrong 24 out of 24 main diagonals are wrong 16 64 out of 64 k*k*k block-corners are wrong 128 192 out of 192 1*k*k block-corners are wrong sublattice 2 : 8 faults 64 out of 64 pantriagonals are noncomplete 001: 0 0 3 32 0 2 0 2 0 0 002: 1 24 0 0 1 1 0 1 1 1 011: 6 96 6 96 6 6 6 6 6 6 012: 6 80 6 96 2 4 0 4 6 6 022: 1 24 0 0 1 1 1 1 1 1 111: 4 48 4 64 0 0 0 0 4 4 112: 6 96 6 96 6 6 6 6 6 6 122: 2 32 3 32 2 2 0 2 0 0 222: 0 8 0 0 0 0 0 0 0 0 pan(2) ratio = 584/992 = 0.588710 panmagic ratio = 64/208 = 0.307692 magic ratio = 52/76 = 0.684211 latin ratio: 80/144 = 0.555556 contains 1 latin cube 11,38,23,58 18,63,14,35 39,10,59,22 62,19,34,15 56,25,44,05 45,04,49,32 28,53,08,41 01,48,29,52 37,12,57,24 64,17,36,13 09,40,21,60 20,61,16,33 26,55,06,43 03,46,31,50 54,27,42,07 47,02,51,30 21. Awani Kumar 2007 4 cub4k21, 21. Awani Kumar 2007 , 11 38 ... 30 0 64 not a path-cube first entry in : (2,4,1) not associated (0 errors) 4 out of 4 main triagonals are wrong 24 out of 24 main diagonals are wrong 16 64 out of 64 k*k*k block-corners are wrong 80 192 out of 192 1*k*k block-corners are wrong sublattice 2 : 8 faults 64 out of 64 pantriagonals are noncomplete 001: 0 0 3 48 0 2 0 2 0 0 002: 1 24 0 0 1 1 0 1 1 1 011: 6 96 6 80 6 6 6 6 2 6 012: 5 80 6 96 2 4 0 4 4 4 022: 1 24 0 0 1 1 1 1 0 1 111: 4 32 4 32 0 0 0 0 4 4 112: 6 96 6 80 6 6 6 6 2 6 122: 3 48 2 32 2 2 0 2 2 2 222: 0 8 0 0 0 0 0 0 0 0 pan(2) ratio = 584/992 = 0.588710 panmagic ratio = 80/208 = 0.384615 magic ratio = 48/76 = 0.631579 latin ratio: 80/144 = 0.555556 contains 1 latin cube 11,38,55,26 40,09,28,53 21,60,41,08 58,23,06,43 50,31,14,35 29,52,33,16 48,01,20,61 03,46,63,18 39,10,27,54 12,37,56,25 57,24,05,44 22,59,42,07 30,51,34,15 49,32,13,36 04,45,64,17 47,02,19,62 22. Awani Kumar 2007 4 cub4k22, 22. Awani Kumar 2007 , 11 38 ... 62 0 64 not a path-cube first entry in : (2,3,2) not associated (0 errors) 0 out of 4 main triagonals are wrong 24 out of 24 main diagonals are wrong 16 64 out of 64 k*k*k block-corners are wrong 96 192 out of 192 1*k*k block-corners are wrong sublattice 2 : 8 faults 64 out of 64 pantriagonals are noncomplete 001: 0 0 2 32 0 2 0 2 0 0 002: 1 24 0 0 1 1 0 1 1 1 011: 6 96 6 80 6 6 6 6 4 6 012: 5 80 5 80 2 4 0 4 4 6 022: 1 24 0 0 1 1 1 1 1 1 111: 4 48 4 64 0 0 0 0 4 4 112: 6 96 6 80 6 6 6 6 4 6 122: 2 32 3 48 2 2 0 2 0 0 222: 0 8 0 0 0 0 0 0 0 0 pan(2) ratio = 584/992 = 0.588710 panmagic ratio = 64/208 = 0.307692 magic ratio = 52/76 = 0.684211 latin ratio: 80/144 = 0.555556 contains 1 latin cube 11,40,57,22 38,09,24,59 27,56,41,06 54,25,08,43 50,29,48,03 31,52,01,46 14,33,20,63 35,16,61,18 39,12,21,58 10,37,60,23 55,28,05,42 26,53,44,07 30,49,04,47 51,32,45,02 34,13,64,19 15,36,17,62 23. Awani Kumar 2007 4 cub4k23, 23. Awani Kumar 2007 , 11 40 ... 62 0 64 not a path-cube first entry in : (2,2,3) not associated (0 errors) 2 out of 4 main triagonals are wrong 24 out of 24 main diagonals are wrong 16 64 out of 64 k*k*k block-corners are wrong 88 192 out of 192 1*k*k block-corners are wrong sublattice 2 : 8 faults 64 out of 64 pantriagonals are noncomplete 001: 0 0 3 40 0 2 0 2 0 0 002: 1 24 0 0 1 1 1 1 1 1 011: 6 96 6 72 6 6 6 6 6 6 012: 6 80 6 88 2 4 2 4 6 6 022: 1 24 0 0 1 1 1 1 1 1 111: 4 48 4 64 0 0 0 0 4 4 112: 6 96 6 88 6 6 6 6 6 6 122: 3 40 3 48 2 2 2 2 0 0 222: 0 8 0 0 0 0 0 0 0 0 pan(2) ratio = 576/992 = 0.580645 panmagic ratio = 64/208 = 0.307692 magic ratio = 50/76 = 0.657895 latin ratio: 80/144 = 0.555556 contains 1 latin cube 17,08,63,42 58,47,24,01 07,50,41,32 48,25,02,55 62,43,20,05 21,04,59,46 44,29,06,51 03,54,45,28 39,18,09,64 16,57,34,23 49,40,31,10 26,15,56,33 12,61,38,19 35,22,13,60 30,11,52,37 53,36,27,14 24. Guenter Stertenbrink 2003 4 cub4k24, 24. Guenter Stertenbrink 2003 , 17 8 ... 14 0 64 not a path-cube first entry in : (1,2,4) not associated (0 errors) 2 out of 4 main triagonals are wrong 24 out of 24 main diagonals are wrong 16 64 out of 64 k*k*k block-corners are wrong 128 192 out of 192 1*k*k block-corners are wrong sublattice 2 : 8 faults 64 out of 64 pantriagonals are noncomplete 001: 0 0 3 32 0 0 0 0 0 0 002: 1 24 0 0 1 1 1 1 1 1 011: 6 96 6 96 6 6 6 6 6 6 012: 6 80 6 96 0 0 2 4 5 6 022: 1 24 0 0 1 1 1 1 1 1 111: 4 48 4 64 0 0 0 4 4 4 112: 6 96 6 96 6 6 6 6 6 6 122: 2 32 2 24 0 0 2 2 0 0 222: 0 8 0 0 0 0 0 0 0 0 pan(2) ratio = 584/992 = 0.588710 panmagic ratio = 64/208 = 0.307692 magic ratio = 50/76 = 0.657895 latin ratio: 144/144 = 1.000000 contains 3 orthogonal latin cubes 17,36,63,14 44,25,06,55 61,16,19,34 08,53,42,27 64,13,18,35 05,56,43,26 20,33,62,15 41,28,07,54 45,32,03,50 24,37,58,11 01,52,47,30 60,09,22,39 04,49,46,31 57,12,23,38 48,29,02,51 21,40,59,10 25. Awani Kumar 2006 4 cub4k25, 25. Awani Kumar 2006 , 17 36 ... 10 0 64 not a path-cube first entry in : (3,3,1) not associated (0 errors) 0 out of 4 main triagonals are wrong 24 out of 24 main diagonals are wrong 24 64 out of 64 k*k*k block-corners are wrong 112 192 out of 192 1*k*k block-corners are wrong sublattice 2 : 8 faults 64 out of 64 pantriagonals are noncomplete 001: 0 0 2 32 0 2 0 2 0 0 002: 1 24 0 0 1 1 0 1 1 1 011: 6 96 6 80 6 6 6 6 6 6 012: 4 64 6 96 2 4 0 4 2 4 022: 1 24 0 0 1 1 1 1 1 1 111: 0 0 4 64 0 0 0 0 0 4 112: 6 96 6 80 6 6 6 6 6 6 122: 3 48 2 32 2 2 0 2 2 2 222: 0 8 0 0 0 0 0 0 0 0 pan(2) ratio = 632/992 = 0.637097 panmagic ratio = 112/208 = 0.538462 magic ratio = 52/76 = 0.684211 latin ratio: 80/144 = 0.555556 contains 1 latin cube 17,36,63,14 44,53,06,27 61,16,19,34 08,25,42,55 64,13,18,35 05,28,43,54 20,33,62,15 41,56,07,26 45,32,03,50 60,37,22,11 01,52,47,30 24,09,58,39 04,49,46,31 21,12,59,38 48,29,02,51 57,40,23,10 26. Awani Kumar 2006 4 cub4k26, 26. Awani Kumar 2006 , 17 36 ... 10 0 64 not a path-cube first entry in : (3,3,1) not associated (0 errors) 4 out of 4 main triagonals are wrong 24 out of 24 main diagonals are wrong 32 64 out of 64 k*k*k block-corners are wrong 112 192 out of 192 1*k*k block-corners are wrong sublattice 2 : 8 faults 64 out of 64 pantriagonals are noncomplete 001: 0 0 3 40 0 2 0 2 0 0 002: 1 24 0 0 1 1 0 1 1 1 011: 6 96 6 88 6 6 6 6 6 6 012: 4 64 6 88 2 4 1 4 3 4 022: 1 24 0 0 1 1 1 1 1 1 111: 4 64 4 64 0 0 4 4 4 4 112: 6 96 6 88 6 6 6 6 6 6 122: 3 48 2 32 2 2 0 2 2 2 222: 0 8 0 0 0 0 0 0 0 0 pan(2) ratio = 568/992 = 0.572581 panmagic ratio = 48/208 = 0.230769 magic ratio = 48/76 = 0.631579 latin ratio: 80/144 = 0.555556 contains 1 latin cube 17,40,63,10 58,15,24,33 07,18,41,64 48,57,02,23 62,11,20,37 21,36,59,14 44,61,06,19 03,22,45,60 39,50,09,32 16,25,34,55 49,08,31,42 26,47,56,01 12,29,38,51 35,54,13,28 30,43,52,05 53,04,27,46 27. Guenter Stertenbrink 2003 4 cub4k27, 27. Guenter Stertenbrink 2003 , 17 40 ... 46 0 64 not a path-cube first entry in : (3,4,4) not associated (0 errors) 2 out of 4 main triagonals are wrong 24 out of 24 main diagonals are wrong 16 64 out of 64 k*k*k block-corners are wrong 128 192 out of 192 1*k*k block-corners are wrong sublattice 2 : 8 faults 64 out of 64 pantriagonals are noncomplete 001: 0 0 3 32 0 0 0 0 0 0 002: 1 24 0 0 1 1 1 1 1 1 011: 6 96 6 96 6 6 6 6 6 6 012: 6 80 6 96 0 0 2 4 5 6 022: 1 24 0 0 1 1 1 1 1 1 111: 4 48 4 64 0 0 0 4 4 4 112: 6 96 6 96 6 6 6 6 6 6 122: 2 32 2 24 0 0 2 2 0 0 222: 0 8 0 0 0 0 0 0 0 0 pan(2) ratio = 584/992 = 0.588710 panmagic ratio = 64/208 = 0.307692 magic ratio = 50/76 = 0.657895 latin ratio: 144/144 = 1.000000 contains 3 orthogonal latin cubes 19,06,61,44 60,45,22,03 37,20,11,62 14,59,36,21 64,41,18,07 23,02,57,48 10,63,40,17 33,24,15,58 05,52,43,30 46,27,04,53 51,38,29,12 28,13,54,35 42,31,08,49 01,56,47,26 32,09,50,39 55,34,25,16 28. Guenter Stertenbrink 2003 4 cub4k28, 28. Guenter Stertenbrink 2003 , 19 6 ... 16 0 64 not a path-cube first entry in : (4,2,1) not associated (0 errors) 2 out of 4 main triagonals are wrong 24 out of 24 main diagonals are wrong 16 64 out of 64 k*k*k block-corners are wrong 128 192 out of 192 1*k*k block-corners are wrong sublattice 2 : 8 faults 64 out of 64 pantriagonals are noncomplete 001: 0 0 3 32 0 0 0 0 0 0 002: 1 24 0 0 1 1 1 1 1 1 011: 6 96 6 96 6 6 6 6 6 6 012: 6 80 5 80 0 0 2 4 5 6 022: 1 24 0 0 1 1 1 1 1 1 111: 4 48 4 64 0 0 0 4 4 4 112: 6 96 6 96 6 6 6 6 6 6 122: 2 32 3 40 0 0 2 2 0 0 222: 0 8 0 0 0 0 0 0 0 0 pan(2) ratio = 584/992 = 0.588710 panmagic ratio = 64/208 = 0.307692 magic ratio = 50/76 = 0.657895 latin ratio: 144/144 = 1.000000 contains 3 orthogonal latin cubes 19,10,63,38 64,37,20,09 45,56,01,28 02,27,46,55 62,39,18,11 17,12,61,40 04,25,48,53 47,54,03,26 15,22,35,58 36,57,16,21 49,44,29,08 30,07,50,43 34,59,14,23 13,24,33,60 32,05,52,41 51,42,31,06 29. Awani Kumar 2007 4 cub4k29, 29. Awani Kumar 2007 , 19 10 ... 6 0 64 not a path-cube first entry in : (1,3,3) not associated (0 errors) 4 out of 4 main triagonals are wrong 24 out of 24 main diagonals are wrong 16 64 out of 64 k*k*k block-corners are wrong 96 192 out of 192 1*k*k block-corners are wrong sublattice 2 : 8 faults 64 out of 64 pantriagonals are noncomplete 001: 0 0 3 48 0 2 0 2 0 0 002: 1 24 0 0 1 1 0 1 1 1 011: 6 96 4 48 6 6 6 6 4 6 012: 4 64 6 96 2 4 0 4 4 6 022: 1 24 0 0 1 1 1 1 1 1 111: 4 48 4 64 0 0 0 0 4 4 112: 6 96 4 48 6 6 6 6 4 6 122: 2 32 3 48 2 2 0 2 0 0 222: 0 8 0 0 0 0 0 0 0 0 pan(2) ratio = 600/992 = 0.604839 panmagic ratio = 64/208 = 0.307692 magic ratio = 48/76 = 0.631579 latin ratio: 80/144 = 0.555556 contains 1 latin cube 19,10,63,38 62,39,18,11 15,58,35,22 34,23,14,59 64,37,20,09 17,12,61,40 36,21,16,57 13,60,33,24 45,28,01,56 04,53,48,25 49,44,29,08 32,05,52,41 02,55,46,27 47,26,03,54 30,07,50,43 51,42,31,06 30. Awani Kumar 2007 4 cub4k30, 30. Awani Kumar 2007 , 19 10 ... 6 0 64 not a path-cube first entry in : (3,1,3) not associated (0 errors) 2 out of 4 main triagonals are wrong 24 out of 24 main diagonals are wrong 16 64 out of 64 k*k*k block-corners are wrong 88 192 out of 192 1*k*k block-corners are wrong sublattice 2 : 8 faults 64 out of 64 pantriagonals are noncomplete 001: 0 0 3 40 0 2 0 2 0 0 002: 1 24 0 0 1 1 1 1 1 1 011: 6 96 6 72 6 6 6 6 6 6 012: 5 72 6 88 2 4 0 4 5 6 022: 1 24 0 0 1 1 1 1 1 1 111: 4 48 4 64 0 0 0 0 4 4 112: 6 96 6 96 6 6 6 6 6 6 122: 2 32 3 48 2 2 0 2 0 0 222: 0 8 0 0 0 0 0 0 0 0 pan(2) ratio = 592/992 = 0.596774 panmagic ratio = 64/208 = 0.307692 magic ratio = 50/76 = 0.657895 latin ratio: 80/144 = 0.555556 contains 1 latin cube 19,16,61,34 06,53,44,27 63,36,17,14 42,25,08,55 62,33,20,15 43,28,05,54 18,13,64,35 07,56,41,26 47,52,01,30 22,37,60,11 03,32,45,50 58,09,24,39 02,29,48,51 59,12,21,38 46,49,04,31 23,40,57,10 31. Awani Kumar 2007 4 cub4k31, 31. Awani Kumar 2007 , 19 16 ... 10 0 64 not a path-cube first entry in : (3,1,3) not associated (0 errors) 4 out of 4 main triagonals are wrong 24 out of 24 main diagonals are wrong 32 64 out of 64 k*k*k block-corners are wrong 112 192 out of 192 1*k*k block-corners are wrong sublattice 2 : 8 faults 64 out of 64 pantriagonals are noncomplete 001: 0 0 3 40 0 2 0 2 0 0 002: 1 24 0 0 1 1 0 1 1 1 011: 6 96 6 88 6 6 6 6 6 6 012: 4 64 6 88 2 4 1 4 3 4 022: 1 24 0 0 1 1 1 1 1 1 111: 4 64 4 64 0 0 4 4 4 4 112: 6 96 6 88 6 6 6 6 6 6 122: 3 48 2 32 2 2 0 2 2 2 222: 0 8 0 0 0 0 0 0 0 0 pan(2) ratio = 568/992 = 0.572581 panmagic ratio = 48/208 = 0.230769 magic ratio = 48/76 = 0.631579 latin ratio: 80/144 = 0.555556 contains 1 latin cube 19,16,61,34 42,53,08,27 63,36,17,14 06,25,44,55 62,33,20,15 07,28,41,54 18,13,64,35 43,56,05,26 47,52,01,30 22,09,60,39 03,32,45,50 58,37,24,11 02,29,48,51 59,40,21,10 46,49,04,31 23,12,57,38 32. Awani Kumar 2007 4 cub4k32, 32. Awani Kumar 2007 , 19 16 ... 38 0 64 not a path-cube first entry in : (3,1,3) not associated (0 errors) 0 out of 4 main triagonals are wrong 24 out of 24 main diagonals are wrong 24 64 out of 64 k*k*k block-corners are wrong 112 192 out of 192 1*k*k block-corners are wrong sublattice 2 : 8 faults 64 out of 64 pantriagonals are noncomplete 001: 0 0 2 32 0 2 0 2 0 0 002: 1 24 0 0 1 1 0 1 1 1 011: 6 96 6 80 6 6 6 6 6 6 012: 4 64 6 96 2 4 0 4 2 4 022: 1 24 0 0 1 1 1 1 1 1 111: 0 0 4 64 0 0 0 0 0 4 112: 6 96 6 80 6 6 6 6 6 6 122: 3 48 2 32 2 2 0 2 2 2 222: 0 8 0 0 0 0 0 0 0 0 pan(2) ratio = 632/992 = 0.637097 panmagic ratio = 112/208 = 0.538462 magic ratio = 52/76 = 0.684211 latin ratio: 80/144 = 0.555556 contains 1 latin cube 19,34,61,16 06,27,44,53 63,14,17,36 42,55,08,25 62,15,20,33 43,54,05,28 18,35,64,13 07,26,41,56 47,30,01,52 22,11,60,37 03,50,45,32 58,39,24,09 02,51,48,29 59,38,21,12 46,31,04,49 23,10,57,40 33. Awani Kumar 2006 4 cub4k33, 33. Awani Kumar 2006 , 19 34 ... 40 0 64 not a path-cube first entry in : (3,1,3) not associated (0 errors) 4 out of 4 main triagonals are wrong 24 out of 24 main diagonals are wrong 32 64 out of 64 k*k*k block-corners are wrong 112 192 out of 192 1*k*k block-corners are wrong sublattice 2 : 8 faults 64 out of 64 pantriagonals are noncomplete 001: 0 0 3 40 0 2 0 2 0 0 002: 1 24 0 0 1 1 0 1 1 1 011: 6 96 6 88 6 6 6 6 6 6 012: 4 64 6 88 2 4 1 4 3 4 022: 1 24 0 0 1 1 1 1 1 1 111: 4 64 4 64 0 0 4 4 4 4 112: 6 96 6 88 6 6 6 6 6 6 122: 3 48 2 32 2 2 0 2 2 2 222: 0 8 0 0 0 0 0 0 0 0 pan(2) ratio = 568/992 = 0.572581 panmagic ratio = 48/208 = 0.230769 magic ratio = 48/76 = 0.631579 latin ratio: 80/144 = 0.555556 contains 1 latin cube 19,42,63,06 34,27,14,55 61,08,17,44 16,53,36,25 62,07,18,43 15,54,35,26 20,41,64,05 33,28,13,56 47,22,03,58 30,39,50,11 01,60,45,24 52,09,32,37 02,59,46,23 51,10,31,38 48,21,04,57 29,40,49,12 34. Awani Kumar 2006 4 cub4k34, 34. Awani Kumar 2006 , 19 42 ... 12 0 64 not a path-cube first entry in : (3,3,1) not associated (0 errors) 0 out of 4 main triagonals are wrong 24 out of 24 main diagonals are wrong 24 64 out of 64 k*k*k block-corners are wrong 112 192 out of 192 1*k*k block-corners are wrong sublattice 2 : 8 faults 64 out of 64 pantriagonals are noncomplete 001: 0 0 2 32 0 2 0 2 0 0 002: 1 24 0 0 1 1 0 1 1 1 011: 6 96 6 80 6 6 6 6 6 6 012: 4 64 6 96 2 4 0 4 2 4 022: 1 24 0 0 1 1 1 1 1 1 111: 0 0 4 64 0 0 0 0 0 4 112: 6 96 6 80 6 6 6 6 6 6 122: 3 48 2 32 2 2 0 2 2 2 222: 0 8 0 0 0 0 0 0 0 0 pan(2) ratio = 632/992 = 0.637097 panmagic ratio = 112/208 = 0.538462 magic ratio = 52/76 = 0.684211 latin ratio: 80/144 = 0.555556 contains 1 latin cube 21,04,59,46 62,43,20,05 03,54,45,28 44,29,06,51 58,47,24,01 17,08,63,42 48,25,02,55 07,50,41,32 35,22,13,60 12,61,38,19 53,36,27,14 30,11,52,37 16,57,34,23 39,18,09,64 26,15,56,33 49,40,31,10 35. Guenter Stertenbrink 2003 4 cub4k35, 35. Guenter Stertenbrink 2003 , 21 4 ... 10 0 64 not a path-cube first entry in : (2,1,4) not associated (0 errors) 2 out of 4 main triagonals are wrong 24 out of 24 main diagonals are wrong 16 64 out of 64 k*k*k block-corners are wrong 128 192 out of 192 1*k*k block-corners are wrong sublattice 2 : 8 faults 64 out of 64 pantriagonals are noncomplete 001: 0 0 3 32 0 0 0 0 0 0 002: 1 24 0 0 1 1 1 1 1 1 011: 6 96 6 96 6 6 6 6 6 6 012: 6 80 6 96 0 0 2 4 5 6 022: 1 24 0 0 1 1 1 1 1 1 111: 4 48 4 64 0 0 0 4 4 4 112: 6 96 6 96 6 6 6 6 6 6 122: 2 32 2 24 0 0 2 2 0 0 222: 0 8 0 0 0 0 0 0 0 0 pan(2) ratio = 584/992 = 0.588710 panmagic ratio = 64/208 = 0.307692 magic ratio = 50/76 = 0.657895 latin ratio: 144/144 = 1.000000 contains 3 orthogonal latin cubes 21,10,47,52 34,61,28,07 15,20,53,42 60,39,02,29 48,51,22,09 27,08,33,62 54,41,16,19 01,30,59,40 11,24,49,46 64,35,06,25 17,14,43,56 38,57,32,03 50,45,12,23 05,26,63,36 44,55,18,13 31,04,37,58 36. Guenter Stertenbrink 2003 4 cub4k36, 36. Guenter Stertenbrink 2003 , 21 10 ... 58 0 64 not a path-cube first entry in : (2,4,1) not associated (0 errors) 0 out of 4 main triagonals are wrong 24 out of 24 main diagonals are wrong 24 64 out of 64 k*k*k block-corners are wrong 112 192 out of 192 1*k*k block-corners are wrong sublattice 2 : 8 faults 64 out of 64 pantriagonals are noncomplete 001: 0 0 2 32 0 0 0 0 0 0 002: 1 24 0 0 1 1 1 1 1 1 011: 6 96 6 80 6 6 6 6 6 6 012: 4 64 6 96 0 0 2 4 2 4 022: 1 24 0 0 1 1 1 1 1 1 111: 0 0 4 64 0 0 0 4 0 4 112: 6 96 6 80 6 6 6 6 6 6 122: 3 48 2 32 0 0 2 2 2 2 222: 0 8 0 0 0 0 0 0 0 0 pan(2) ratio = 632/992 = 0.637097 panmagic ratio = 112/208 = 0.538462 magic ratio = 52/76 = 0.684211 latin ratio: 144/144 = 1.000000 contains 3 orthogonal latin cubes 21,16,43,50 02,27,64,37 47,54,17,12 60,33,06,31 42,51,24,13 61,40,03,26 20,09,46,55 07,30,57,36 15,22,49,44 28,01,38,63 53,48,11,18 34,59,32,05 52,41,14,23 39,62,25,04 10,19,56,45 29,08,35,58 37. Guenter Stertenbrink 2003 4 cub4k37, 37. Guenter Stertenbrink 2003 , 21 16 ... 58 0 64 not a path-cube first entry in : (3,2,2) not associated (0 errors) 0 out of 4 main triagonals are wrong 24 out of 24 main diagonals are wrong 24 64 out of 64 k*k*k block-corners are wrong 128 192 out of 192 1*k*k block-corners are wrong sublattice 2 : 8 faults 64 out of 64 pantriagonals are noncomplete 001: 0 0 3 48 0 0 0 0 0 0 002: 1 24 0 0 1 1 1 1 0 1 011: 6 96 6 96 6 6 6 6 6 6 012: 3 48 5 80 0 0 2 4 2 4 022: 1 24 0 0 1 1 1 1 1 1 111: 4 32 4 32 0 0 0 4 4 4 112: 6 96 4 64 6 6 6 6 6 6 122: 2 32 2 32 0 0 2 2 0 2 222: 0 8 0 0 0 0 0 0 0 0 pan(2) ratio = 632/992 = 0.637097 panmagic ratio = 80/208 = 0.384615 magic ratio = 52/76 = 0.684211 latin ratio: 144/144 = 1.000000 contains 3 orthogonal latin cubes 23,10,57,40 02,51,48,29 59,38,21,12 46,31,04,49 58,39,24,09 47,30,01,52 22,11,60,37 03,50,45,32 07,26,41,56 62,15,20,33 43,54,05,28 18,35,64,13 42,55,08,25 19,34,61,16 06,27,44,53 63,14,17,36 38. Awani Kumar 2006 4 cub4k38, 38. Awani Kumar 2006 , 23 10 ... 36 0 64 not a path-cube first entry in : (2,2,3) not associated (0 errors) 4 out of 4 main triagonals are wrong 24 out of 24 main diagonals are wrong 32 64 out of 64 k*k*k block-corners are wrong 112 192 out of 192 1*k*k block-corners are wrong sublattice 2 : 8 faults 64 out of 64 pantriagonals are noncomplete 001: 0 0 3 40 0 2 0 2 0 0 002: 1 24 0 0 1 1 0 1 1 1 011: 6 96 6 88 6 6 6 6 6 6 012: 5 80 6 88 2 4 2 4 4 4 022: 1 24 0 0 1 1 1 1 1 1 111: 4 64 4 64 0 0 4 4 4 4 112: 6 96 6 88 6 6 6 6 6 6 122: 3 48 2 32 2 2 0 2 2 2 222: 0 8 0 0 0 0 0 0 0 0 pan(2) ratio = 552/992 = 0.556452 panmagic ratio = 48/208 = 0.230769 magic ratio = 48/76 = 0.631579 latin ratio: 80/144 = 0.555556 contains 1 latin cube 23,40,57,10 02,29,48,51 59,12,21,38 46,49,04,31 58,09,24,39 47,52,01,30 22,37,60,11 03,32,45,50 07,56,41,26 62,33,20,15 43,28,05,54 18,13,64,35 42,25,08,55 19,16,61,34 06,53,44,27 63,36,17,14 39. Awani Kumar 2007 4 cub4k39, 39. Awani Kumar 2007 , 23 40 ... 14 0 64 not a path-cube first entry in : (2,2,3) not associated (0 errors) 4 out of 4 main triagonals are wrong 24 out of 24 main diagonals are wrong 32 64 out of 64 k*k*k block-corners are wrong 112 192 out of 192 1*k*k block-corners are wrong sublattice 2 : 8 faults 64 out of 64 pantriagonals are noncomplete 001: 0 0 3 40 0 2 0 2 0 0 002: 1 24 0 0 1 1 0 1 1 1 011: 6 96 6 88 6 6 6 6 6 6 012: 5 80 6 88 2 4 2 4 4 4 022: 1 24 0 0 1 1 1 1 1 1 111: 4 64 4 64 0 0 4 4 4 4 112: 6 96 6 88 6 6 6 6 6 6 122: 3 48 2 32 2 2 0 2 2 2 222: 0 8 0 0 0 0 0 0 0 0 pan(2) ratio = 552/992 = 0.556452 panmagic ratio = 48/208 = 0.230769 magic ratio = 48/76 = 0.631579 latin ratio: 80/144 = 0.555556 contains 1 latin cube 27,02,55,46 56,45,28,01 37,64,09,20 10,19,38,63 54,47,26,03 25,04,53,48 12,17,40,61 39,62,11,18 07,30,43,50 44,49,08,29 57,36,21,16 22,15,58,35 42,51,06,31 05,32,41,52 24,13,60,33 59,34,23,14 40. Awani Kumar 2007 4 cub4k40, 40. Awani Kumar 2007 , 27 2 ... 14 0 64 not a path-cube first entry in : (1,2,4) not associated (0 errors) 4 out of 4 main triagonals are wrong 24 out of 24 main diagonals are wrong 16 64 out of 64 k*k*k block-corners are wrong 96 192 out of 192 1*k*k block-corners are wrong sublattice 2 : 8 faults 64 out of 64 pantriagonals are noncomplete 001: 0 0 3 48 0 2 0 2 0 0 002: 1 24 0 0 1 1 0 1 1 1 011: 6 96 4 48 6 6 6 6 4 6 012: 4 64 6 96 2 4 0 4 4 6 022: 1 24 0 0 1 1 1 1 1 1 111: 4 48 4 64 0 0 0 0 4 4 112: 6 96 4 48 6 6 6 6 4 6 122: 2 32 3 48 2 2 0 2 0 0 222: 0 8 0 0 0 0 0 0 0 0 pan(2) ratio = 600/992 = 0.604839 panmagic ratio = 64/208 = 0.307692 magic ratio = 48/76 = 0.631579 latin ratio: 80/144 = 0.555556 contains 1 latin cube 27,02,55,46 54,47,26,03 43,30,07,50 06,51,42,31 56,45,28,01 25,04,53,48 08,49,44,29 41,32,05,52 09,64,37,20 40,17,12,61 57,36,21,16 24,13,60,33 38,19,10,63 11,62,39,18 22,15,58,35 59,34,23,14 41. Awani Kumar 2007 4 cub4k41, 41. Awani Kumar 2007 , 27 2 ... 14 0 64 not a path-cube first entry in : (2,1,4) not associated (0 errors) 2 out of 4 main triagonals are wrong 24 out of 24 main diagonals are wrong 16 64 out of 64 k*k*k block-corners are wrong 88 192 out of 192 1*k*k block-corners are wrong sublattice 2 : 8 faults 64 out of 64 pantriagonals are noncomplete 001: 0 0 3 40 0 2 0 2 0 0 002: 1 24 0 0 1 1 1 1 1 1 011: 6 96 6 72 6 6 6 6 6 6 012: 6 88 6 88 2 4 2 4 5 6 022: 1 24 0 0 1 1 0 1 1 1 111: 4 48 4 64 0 0 0 0 4 4 112: 6 96 6 80 6 6 4 6 6 6 122: 3 48 1 16 2 2 2 2 0 0 222: 0 8 0 0 0 0 0 0 0 0 pan(2) ratio = 560/992 = 0.564516 panmagic ratio = 64/208 = 0.307692 magic ratio = 50/76 = 0.657895 latin ratio: 80/144 = 0.555556 contains 1 latin cube 27,08,53,42 34,61,16,19 55,44,25,06 14,17,36,63 54,41,28,07 15,20,33,62 26,05,56,43 35,64,13,18 39,60,09,22 30,01,52,47 11,24,37,58 50,45,32,03 10,21,40,59 51,48,29,02 38,57,12,23 31,04,49,46 42. Awani Kumar 2007 4 cub4k42, 42. Awani Kumar 2007 , 27 8 ... 46 0 64 not a path-cube first entry in : (3,2,2) not associated (0 errors) 0 out of 4 main triagonals are wrong 24 out of 24 main diagonals are wrong 24 64 out of 64 k*k*k block-corners are wrong 112 192 out of 192 1*k*k block-corners are wrong sublattice 2 : 8 faults 64 out of 64 pantriagonals are noncomplete 001: 0 0 2 32 0 2 0 2 0 0 002: 1 24 0 0 1 1 0 1 1 1 011: 6 96 6 80 6 6 6 6 6 6 012: 4 64 6 96 2 4 0 4 2 4 022: 1 24 0 0 1 1 1 1 1 1 111: 0 0 4 64 0 0 0 0 0 4 112: 6 96 6 80 6 6 6 6 6 6 122: 3 48 2 32 2 2 0 2 2 2 222: 0 8 0 0 0 0 0 0 0 0 pan(2) ratio = 632/992 = 0.637097 panmagic ratio = 112/208 = 0.538462 magic ratio = 52/76 = 0.684211 latin ratio: 80/144 = 0.555556 contains 1 latin cube 27,34,55,14 40,29,12,49 05,64,41,20 58,03,22,47 54,15,26,35 09,52,37,32 44,17,08,61 23,46,59,02 39,30,11,50 28,33,56,13 57,04,21,48 06,63,42,19 10,51,38,31 53,16,25,36 24,45,60,01 43,18,07,62 43. Awani Kumar 2007 4 cub4k43, 43. Awani Kumar 2007 , 27 34 ... 62 0 64 not a path-cube first entry in : (4,3,4) not associated (0 errors) 4 out of 4 main triagonals are wrong 24 out of 24 main diagonals are wrong 16 64 out of 64 k*k*k block-corners are wrong 96 192 out of 192 1*k*k block-corners are wrong sublattice 2 : 8 faults 64 out of 64 pantriagonals are noncomplete 001: 0 0 3 48 0 2 0 2 0 0 002: 1 24 0 0 1 1 0 1 1 1 011: 6 96 6 80 6 6 6 6 4 6 012: 5 80 5 80 2 4 0 4 4 6 022: 1 24 0 0 1 1 1 1 1 1 111: 4 48 4 64 0 0 0 0 4 4 112: 6 96 6 80 6 6 6 6 4 6 122: 2 32 2 32 2 2 0 2 0 0 222: 0 8 0 0 0 0 0 0 0 0 pan(2) ratio = 584/992 = 0.588710 panmagic ratio = 64/208 = 0.307692 magic ratio = 48/76 = 0.631579 latin ratio: 80/144 = 0.555556 contains 1 latin cube 27,38,55,10 40,09,28,53 05,60,41,24 58,23,06,43 50,15,30,35 29,52,33,16 48,17,04,61 03,46,63,18 39,26,11,54 12,37,56,25 57,08,21,44 22,59,42,07 14,51,34,31 49,32,13,36 20,45,64,01 47,02,19,62 44. Awani Kumar 2007 4 cub4k44, 44. Awani Kumar 2007 , 27 38 ... 62 0 64 not a path-cube first entry in : (4,3,4) not associated (0 errors) 4 out of 4 main triagonals are wrong 24 out of 24 main diagonals are wrong 16 64 out of 64 k*k*k block-corners are wrong 128 192 out of 192 1*k*k block-corners are wrong sublattice 2 : 8 faults 64 out of 64 pantriagonals are noncomplete 001: 0 0 3 32 0 2 0 2 0 0 002: 1 24 0 0 1 1 0 1 1 1 011: 6 96 6 96 6 6 6 6 6 6 012: 6 80 6 88 2 4 0 4 5 6 022: 1 24 0 0 1 1 1 1 1 1 111: 4 48 4 64 0 0 0 0 4 4 112: 6 96 6 96 6 6 6 6 6 6 122: 2 32 3 32 2 2 0 2 0 0 222: 0 8 0 0 0 0 0 0 0 0 pan(2) ratio = 584/992 = 0.588710 panmagic ratio = 64/208 = 0.307692 magic ratio = 48/76 = 0.631579 latin ratio: 80/144 = 0.555556 contains 1 latin cube 33,16,61,20 52,29,48,01 15,34,19,62 30,51,02,47 60,21,40,09 41,08,53,28 22,59,10,39 07,42,27,54 13,36,17,64 32,49,04,45 35,14,63,18 50,31,46,03 24,57,12,37 05,44,25,56 58,23,38,11 43,06,55,26 45. Awani Kumar 2006 4 cub4k45, 45. Awani Kumar 2006 , 33 16 ... 26 0 64 not a path-cube first entry in : (1,2,4) not associated (0 errors) 0 out of 4 main triagonals are wrong 24 out of 24 main diagonals are wrong 16 64 out of 64 k*k*k block-corners are wrong 80 192 out of 192 1*k*k block-corners are wrong sublattice 2 : 8 faults 64 out of 64 pantriagonals are noncomplete 001: 0 0 3 48 0 2 0 2 0 0 002: 1 24 0 0 1 1 0 1 1 1 011: 6 96 6 80 6 6 6 6 2 6 012: 5 80 6 96 2 4 0 4 4 4 022: 1 24 0 0 1 1 1 1 0 1 111: 4 32 4 32 0 0 0 0 4 4 112: 6 96 6 80 6 6 6 6 2 6 122: 3 48 2 32 2 2 0 2 2 2 222: 0 8 0 0 0 0 0 0 0 0 pan(2) ratio = 584/992 = 0.588710 panmagic ratio = 80/208 = 0.384615 magic ratio = 52/76 = 0.684211 latin ratio: 80/144 = 0.555556 contains 1 latin cube 35,14,63,18 22,59,38,11 15,34,19,62 58,23,10,39 50,31,46,03 43,06,27,54 30,51,02,47 07,42,55,26 13,36,17,64 60,21,12,37 33,16,61,20 24,57,40,09 32,49,04,45 05,44,53,28 52,29,48,01 41,08,25,56 46. Awani Kumar 2006 4 cub4k46, 46. Awani Kumar 2006 , 35 14 ... 56 0 64 not a path-cube first entry in : (4,3,4) not associated (0 errors) 4 out of 4 main triagonals are wrong 24 out of 24 main diagonals are wrong 32 64 out of 64 k*k*k block-corners are wrong 112 192 out of 192 1*k*k block-corners are wrong sublattice 2 : 8 faults 64 out of 64 pantriagonals are noncomplete 001: 0 0 3 40 0 2 0 2 0 0 002: 1 24 0 0 1 1 0 1 1 1 011: 6 96 6 96 6 6 6 6 6 6 012: 5 80 6 96 2 4 2 4 4 4 022: 1 24 0 0 1 1 1 1 1 1 111: 4 64 4 64 0 0 4 4 4 4 112: 6 96 6 88 6 6 6 6 6 6 122: 3 48 2 24 2 2 0 2 2 2 222: 0 8 0 0 0 0 0 0 0 0 pan(2) ratio = 552/992 = 0.556452 panmagic ratio = 48/208 = 0.230769 magic ratio = 48/76 = 0.631579 latin ratio: 80/144 = 0.555556 contains 1 latin cube 35,14,63,18 50,31,46,03 13,36,17,64 32,49,04,45 58,23,38,11 43,06,55,26 24,57,12,37 05,44,25,56 15,34,19,62 30,51,02,47 33,16,61,20 52,29,48,01 22,59,10,39 07,42,27,54 60,21,40,09 41,08,53,28 47. Awani Kumar 2006 4 cub4k47, 47. Awani Kumar 2006 , 35 14 ... 28 0 64 not a path-cube first entry in : (3,4,4) not associated (0 errors) 0 out of 4 main triagonals are wrong 24 out of 24 main diagonals are wrong 16 64 out of 64 k*k*k block-corners are wrong 80 192 out of 192 1*k*k block-corners are wrong sublattice 2 : 8 faults 64 out of 64 pantriagonals are noncomplete 001: 0 0 3 48 0 2 0 2 0 0 002: 1 24 0 0 1 1 0 1 1 1 011: 6 96 6 80 6 6 6 6 2 6 012: 5 80 6 96 2 4 0 4 4 4 022: 1 24 0 0 1 1 1 1 0 1 111: 4 32 4 32 0 0 0 0 4 4 112: 6 96 6 80 6 6 6 6 2 6 122: 3 48 2 32 2 2 0 2 2 2 222: 0 8 0 0 0 0 0 0 0 0 pan(2) ratio = 584/992 = 0.588710 panmagic ratio = 80/208 = 0.384615 magic ratio = 52/76 = 0.684211 latin ratio: 80/144 = 0.555556 contains 1 latin cube 37,26,63,04 50,13,44,23 31,36,05,58 12,55,18,45 64,03,38,25 43,24,49,14 06,57,32,35 17,46,11,56 27,40,01,62 16,51,22,41 33,30,59,08 54,09,48,19 02,61,28,39 21,42,15,52 60,07,34,29 47,20,53,10 48. Guenter Stertenbrink 2003 4 cub4k48, 48. Guenter Stertenbrink 2003 , 37 26 ... 10 0 64 not a path-cube first entry in : (3,1,3) not associated (0 errors) 0 out of 4 main triagonals are wrong 24 out of 24 main diagonals are wrong 24 64 out of 64 k*k*k block-corners are wrong 128 192 out of 192 1*k*k block-corners are wrong sublattice 2 : 8 faults 64 out of 64 pantriagonals are noncomplete 001: 0 0 3 48 0 0 0 0 0 0 002: 1 24 0 0 1 1 1 1 0 1 011: 6 96 6 96 6 6 6 6 6 6 012: 3 48 5 80 0 0 2 4 2 4 022: 1 24 0 0 1 1 1 1 1 1 111: 4 32 4 32 0 0 0 4 4 4 112: 6 96 4 64 6 6 6 6 6 6 122: 2 32 2 32 0 0 2 2 0 2 222: 0 8 0 0 0 0 0 0 0 0 pan(2) ratio = 632/992 = 0.637097 panmagic ratio = 80/208 = 0.384615 magic ratio = 52/76 = 0.684211 latin ratio: 144/144 = 1.000000 contains 3 orthogonal latin cubes 37,32,59,02 18,43,16,53 63,06,33,28 12,49,22,47 58,03,40,29 13,56,19,42 36,25,62,07 23,46,09,52 31,38,01,60 44,17,54,15 05,64,27,34 50,11,48,21 04,57,30,39 55,14,41,20 26,35,08,61 45,24,51,10 49. Guenter Stertenbrink 2003 4 cub4k49, 49. Guenter Stertenbrink 2003 , 37 32 ... 10 0 64 not a path-cube first entry in : (3,1,3) not associated (0 errors) 0 out of 4 main triagonals are wrong 24 out of 24 main diagonals are wrong 24 64 out of 64 k*k*k block-corners are wrong 112 192 out of 192 1*k*k block-corners are wrong sublattice 2 : 8 faults 64 out of 64 pantriagonals are noncomplete 001: 0 0 2 32 0 0 0 0 0 0 002: 1 24 0 0 1 1 1 1 1 1 011: 6 96 6 80 6 6 6 6 6 6 012: 4 64 6 96 0 0 2 4 2 4 022: 1 24 0 0 1 1 1 1 1 1 111: 0 0 4 64 0 0 0 4 0 4 112: 6 96 6 80 6 6 6 6 6 6 122: 3 48 2 32 0 0 2 2 2 2 222: 0 8 0 0 0 0 0 0 0 0 pan(2) ratio = 632/992 = 0.637097 panmagic ratio = 112/208 = 0.538462 magic ratio = 52/76 = 0.684211 latin ratio: 144/144 = 1.000000 contains 3 orthogonal latin cubes 49,12,29,40 04,57,48,21 31,38,51,10 46,23,02,59 32,37,52,09 45,24,01,60 50,11,30,39 03,58,47,22 13,56,33,28 64,05,20,41 35,26,15,54 18,43,62,07 36,25,16,53 17,44,61,08 14,55,34,27 63,06,19,42 50. Awani Kumar 2006 4 cub4k50, 50. Awani Kumar 2006 , 49 12 ... 42 0 64 not a path-cube first entry in : (2,2,3) not associated (0 errors) 0 out of 4 main triagonals are wrong 24 out of 24 main diagonals are wrong 24 64 out of 64 k*k*k block-corners are wrong 112 192 out of 192 1*k*k block-corners are wrong sublattice 2 : 8 faults 64 out of 64 pantriagonals are noncomplete 001: 0 0 2 32 0 2 0 2 0 0 002: 1 24 0 0 1 1 0 1 1 1 011: 6 96 6 80 6 6 6 6 6 6 012: 4 64 6 96 2 4 0 4 2 4 022: 1 24 0 0 1 1 1 1 1 1 111: 0 0 4 64 0 0 0 0 0 4 112: 6 96 6 80 6 6 6 6 6 6 122: 3 48 2 32 2 2 0 2 2 2 222: 0 8 0 0 0 0 0 0 0 0 pan(2) ratio = 632/992 = 0.637097 panmagic ratio = 112/208 = 0.538462 magic ratio = 52/76 = 0.684211 latin ratio: 80/144 = 0.555556 contains 1 latin cube 51,02,29,48 38,59,12,21 31,46,49,04 10,23,40,57 30,47,52,01 11,22,37,60 50,03,32,45 39,58,09,24 15,62,33,20 54,43,28,05 35,18,13,64 26,07,56,41 34,19,16,61 27,06,53,44 14,63,36,17 55,42,25,08 51. Awani Kumar 2006 4 cub4k51, 51. Awani Kumar 2006 , 51 2 ... 8 0 64 not a path-cube first entry in : (2,1,4) not associated (0 errors) 4 out of 4 main triagonals are wrong 24 out of 24 main diagonals are wrong 32 64 out of 64 k*k*k block-corners are wrong 112 192 out of 192 1*k*k block-corners are wrong sublattice 2 : 8 faults 64 out of 64 pantriagonals are noncomplete 001: 0 0 3 40 0 2 0 2 0 0 002: 1 24 0 0 1 1 0 1 1 1 011: 6 96 6 88 6 6 6 6 6 6 012: 4 64 6 88 2 4 1 4 3 4 022: 1 24 0 0 1 1 1 1 1 1 111: 4 64 4 64 0 0 4 4 4 4 112: 6 96 6 88 6 6 6 6 6 6 122: 3 48 2 32 2 2 0 2 2 2 222: 0 8 0 0 0 0 0 0 0 0 pan(2) ratio = 568/992 = 0.572581 panmagic ratio = 48/208 = 0.230769 magic ratio = 48/76 = 0.631579 latin ratio: 80/144 = 0.555556 contains 1 latin cube 51,10,31,38 02,59,46,23 29,40,49,12 48,21,04,57 30,39,50,11 47,22,03,58 52,09,32,37 01,60,45,24 15,54,35,26 62,07,18,43 33,28,13,56 20,41,64,05 34,27,14,55 19,42,63,06 16,53,36,25 61,08,17,44 52. Awani Kumar 2006 4 cub4k52, 52. Awani Kumar 2006 , 51 10 ... 44 0 64 not a path-cube first entry in : (2,4,1) not associated (0 errors) 0 out of 4 main triagonals are wrong 24 out of 24 main diagonals are wrong 24 64 out of 64 k*k*k block-corners are wrong 112 192 out of 192 1*k*k block-corners are wrong sublattice 2 : 8 faults 64 out of 64 pantriagonals are noncomplete 001: 0 0 2 32 0 2 0 2 0 0 002: 1 24 0 0 1 1 0 1 1 1 011: 6 96 6 80 6 6 6 6 6 6 012: 4 64 6 96 2 4 0 4 2 4 022: 1 24 0 0 1 1 1 1 1 1 111: 0 0 4 64 0 0 0 0 0 4 112: 6 96 6 80 6 6 6 6 6 6 122: 3 48 2 32 2 2 0 2 2 2 222: 0 8 0 0 0 0 0 0 0 0 pan(2) ratio = 632/992 = 0.637097 panmagic ratio = 112/208 = 0.538462 magic ratio = 52/76 = 0.684211 latin ratio: 80/144 = 0.555556 contains 1 latin cube 53,10,47,20 34,29,60,07 15,52,21,42 28,39,02,61 48,19,54,09 59,08,33,30 22,41,16,51 01,62,27,40 11,56,17,46 32,35,06,57 49,14,43,24 38,25,64,03 18,45,12,55 05,58,31,36 44,23,50,13 63,04,37,26 53. Guenter Stertenbrink 2003 4 cub4k53, 53. Guenter Stertenbrink 2003 , 53 10 ... 26 0 64 not a path-cube first entry in : (2,4,1) not associated (0 errors) 0 out of 4 main triagonals are wrong 24 out of 24 main diagonals are wrong 24 64 out of 64 k*k*k block-corners are wrong 128 192 out of 192 1*k*k block-corners are wrong sublattice 2 : 8 faults 64 out of 64 pantriagonals are noncomplete 001: 0 0 3 48 0 0 0 0 0 0 002: 1 24 0 0 1 1 1 1 0 1 011: 6 96 6 96 6 6 6 6 6 6 012: 3 48 5 80 0 0 2 4 2 4 022: 1 24 0 0 1 1 1 1 1 1 111: 4 32 4 32 0 0 0 4 4 4 112: 6 96 4 64 6 6 6 6 6 6 122: 2 32 2 32 0 0 2 2 0 2 222: 0 8 0 0 0 0 0 0 0 0 pan(2) ratio = 632/992 = 0.637097 panmagic ratio = 80/208 = 0.384615 magic ratio = 52/76 = 0.684211 latin ratio: 144/144 = 1.000000 contains 3 orthogonal latin cubes 53,16,43,18 02,59,32,37 47,22,49,12 28,33,06,63 42,19,56,13 29,40,03,58 52,09,46,23 07,62,25,36 15,54,17,44 60,01,38,31 21,48,11,50 34,27,64,05 20,41,14,55 39,30,57,04 10,51,24,45 61,08,35,26 54. Guenter Stertenbrink 2003 4 cub4k54, 54. Guenter Stertenbrink 2003 , 53 16 ... 26 0 64 not a path-cube first entry in : (3,2,2) not associated (0 errors) 0 out of 4 main triagonals are wrong 24 out of 24 main diagonals are wrong 24 64 out of 64 k*k*k block-corners are wrong 112 192 out of 192 1*k*k block-corners are wrong sublattice 2 : 8 faults 64 out of 64 pantriagonals are noncomplete 001: 0 0 2 32 0 0 0 0 0 0 002: 1 24 0 0 1 1 1 1 1 1 011: 6 96 6 80 6 6 6 6 6 6 012: 4 64 6 96 0 0 2 4 2 4 022: 1 24 0 0 1 1 1 1 1 1 111: 0 0 4 64 0 0 0 4 0 4 112: 6 96 6 80 6 6 6 6 6 6 122: 3 48 2 32 0 0 2 2 2 2 222: 0 8 0 0 0 0 0 0 0 0 pan(2) ratio = 632/992 = 0.637097 panmagic ratio = 112/208 = 0.538462 magic ratio = 52/76 = 0.684211 latin ratio: 144/144 = 1.000000 contains 3 orthogonal latin cubes 03,20,47,62 28,09,54,39 45,64,03,18 56,37,26,11 48,61,02,19 53,40,27,10 04,17,46,63 25,12,55,38 29,16,51,34 08,21,42,59 49,36,31,14 44,57,06,23 52,33,30,15 41,60,07,22 32,13,50,35 05,24,43,58 1. Awani Kumar 2006 4 cub4k01, 1. Awani Kumar 2006 , 1 20 ... 58 0 64 not a path-cube first entry in : (1,1,1) not associated (0 errors) 0 out of 4 main triagonals are wrong 24 out of 24 main diagonals are wrong 16 64 out of 64 k*k*k block-corners are wrong 80 192 out of 192 1*k*k block-corners are wrong sublattice 2 : 8 faults 64 out of 64 pantriagonals are noncomplete 001: 0 0 3 48 0 2 0 2 0 0 002: 1 24 0 0 1 1 0 1 1 1 011: 6 96 6 80 6 6 6 6 2 6 012: 5 80 6 96 2 4 0 4 4 4 022: 1 24 0 0 1 1 1 1 0 1 111: 4 32 4 32 0 0 0 0 4 4 112: 6 96 6 80 6 6 6 6 2 6 122: 3 48 2 32 2 2 0 2 2 2 222: 0 8 0 0 0 0 0 0 0 0 pan(2) ratio = 584/992 = 0.588710 panmagic ratio = 80/208 = 0.384615 magic ratio = 52/76 = 0.684211 latin ratio: 80/144 = 0.555556 contains 1 latin cube