From cube-lovers-errors@mc.lcs.mit.edu Mon Nov 2 14:41:00 1998 Return-Path: Received: from sun28.aic.nrl.navy.mil by mc.lcs.mit.edu (8.8.8/mc) with SMTP id OAA00366; Mon, 2 Nov 1998 14:41:00 -0500 (EST) Precedence: bulk Date: Sat, 31 Oct 1998 23:06:34 -0400 (EDT) From: Jerry Bryan Subject: All the Local Maxima at 12q To: Cube-Lovers Message-Id: I had originally decided not to post all the 12q local maxima because there are so many and because not all of them look all that interesting. But I have been looking at them a bit more, and I think it's worth the effort. Some of them will be very familiar and some of them not. I would highlight the following ones. #9 is a partial isoglyph -- four short T's (or four short U's). #57 is the well-known four spot. #68 is one of the more striking of several pseudo two spots. #80 is worthy of some study. It's the only one where the maximality of the inverse is 11 -- almost but not quite a local maximum. #97 along with #98 and #99 are very striking pseudo six spots. #97 and #99 are almost the same pattern, and it took me a while to see how they differ. In the table below, the right most column gives the maximality of the inverse of the pattern, where the maximality is the number of moves which go closer to Start. The maximality of the inverse gives an indication of how close the inverse comes to being a local maximum, with 12 indicating a local maximum. (The maximality of the pattern itself is not given, since it is 12 by definition.) The table gives the 103 local maxima of length 12q which are unique up to symmetry. 1. F F L L F F B B R R B B 12 2. F B' U U D D F' B R R L L 12 3. F B R R F' B' U D L L U' D' 12 4. U' R' L B L B' R L' D L' U D' 12 5. F B R R L L F B U U D D 12 6. R L' F F B B R L' F F B B 12 7. F F B B U U D D R R L L 12 8. R L' U' D F' B R R L L U' D 12 9. F B U U D D F' B R R L L 12 10. U B' D F D' B' D F' D' B B U' 12 11. L B B R D D R' L B B L L 12 12. U R' U L' U' R' U L U' R R U' 12 13. F F U' D R R U D D B B D' 12 14. F B D D F B' L L U U F F 12 15. U D' F U D R' L' U D F U D' 12 16. U U R L F' B' U D' R R L L 10 17. R R U D F' B U' D F B' U' D 8 18. U U D D F B' R R L L B B 12 19. R' L F' B U U F F B B U' D' 12 20. U D' F F U' D R L F B' U' D 12 21. F B R' L D D F B' R' L U' D 12 22. L L U D' B B R L U' D B B 12 23. F L L F' D D F B' L L B B 12 24. F' R R F' U U F' B L L B B 12 25. F B U U L L B B L L U U 8 26. U' D' R L' F F B B L L U' D 4 27. U D R L' F F B B L L U D' 4 28. F B' U U B B L L B B U U 12 29. F' B U D L L B B R R U D 12 30. F' B U D R R F F L L U D 12 31. F B' U U F F R R F F U U 12 32. F B' U U L L B B L L U U 12 33. F B' U U R R F F R R U U 12 34. L L U D L L F' B R L U U 10 35. F' R R F U U F B' R R B B 12 36. L L F' B D D R R F F B B 12 37. L L F' B D D F F B B L L 12 38. D D F' B U D' F F B B U D' 10 39. F F R' L F B' U' D F F L L 12 40. U R' L F U D' R' L F F B B 8 41. U D R L F B' U D' R' L F F 12 42. U D F F U' D R L F B' U' D 12 43. U D B B U' D R' L' F B' U' D 12 44. F F R L' F B' U D' F F L L 12 45. U D F' B R L U' D B B U' D 12 46. U D F' B R' L' U' D F F U' D 12 47. F B' D R' L' U U R L D B B 8 48. B' U' D R' L B' U' D R R L L 6 49. B' U D' R L' F U D' R R L L 6 50. U D F' B' U' D L L F B' U' D' 8 51. U' F' U' D F B' U' D R R L L 2 52. U' F F B R' L U' D F F B B 8 53. D R R L F' B U' D R R L L 2 54. R U' F' B R L' U D' F F U D' 2 55. L F F B R L' F B' R R L L 2 56. L F F B U D' R' L F F B B 8 57. F B' U U D D F B' R R L L 12 58. F B' R L' U' D F' B' R L' U' D' 12 59. F B R L U D' F B R' L' U D' 12 60. F B' U U D D F' B U U D D 12 61. R L' U' D F' B L L U' D F F 12 62. R L B B U D' R R F B U D' 12 63. F B' U D' R L' F F B B U D' 12 64. F B R R L L U D' R' L' U D' 12 65. F B' U D' R L' B B U D' L L 12 66. F F U' D R R U D F F U U 12 67. F L L B U U F' B L L F F 12 68. B R L F F R' L' B U U L L 12 69. U' F B' L' U D' R L' F F B B 2 70. F B R' L' U D' F' B' R' L' U' D' 12 71. F B R L U D' F B R' L' U' D' 12 72. U' R L' U' D F B' R R L L U' 12 73. F' B R' L U' D B R' L U' D D 12 74. U' R' L F B' U' D F B B U' D 6 75. U R' L F' B U D' B F F U D' 6 76. F B U D R' L F F R' L U' D 12 77. R' L' F' B R R L L U D B B 12 78. R L F B' R R L L U' D' F F 12 79. F F R R F' B' U' D' L L U D 8 80. U U R' L F' B' U' D R R L L 11 81. U U D R L' B U D' R R L L 6 82. U D F' B U' D F B' U' D R R 12 83. F B' U D R L' B B R L' U' D 12 84. U D' F F U D' R' L' F B' U' D 12 85. B R L' D' F B' U D' R R L L 2 86. F' R' L U' F B' R' L U D' B B 12 87. F' R' L U' F' B R' L U' D B B 12 88. R' L F B' U D R R L L D D 12 89. F B R L' F' B R L' U D' F F 12 90. U' D' R L' F F U D' R R L L 12 91. F F R' L F' B' U' D' L L B B 10 92. F U D B B U' D' F R L U D' 10 93. R L U D' F B' R' L' F B' U' D 8 94. F B' U' D L L F B' U' D' F F 10 95. F B' U U D D F B' R' L' U D' 10 96. R' L L F' B U R L' F F B B 6 97. F B' U' D R L F' B U U B B 12 98. F B U' D R' L F' B D D B B 12 99. F B' U' D R L F B' D D F F 12 100. U' D F B' U D' F F B B U D' 12 101. U R L' F' U D' R L' F F B B 8 102. U D' R L' F' B U D' F F B B 12 103. F' B' L L U' D F B U' D R R 8 = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = Robert G. Bryan (Jerry Bryan) jbryan@pstcc.cc.tn.us Pellissippi State (423) 539-7198 10915 Hardin Valley Road (423) 694-6435 (fax) P.O. Box 22990 Knoxville, TN 37933-0990