# cube_and_pamball

Mar 12th, 2012
142
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1. cube := Group(
2. ( 1, 3, 8, 6)( 2, 5, 7, 4)
3. ( 9,33,25,17)(10,34,26,18)(11,35,27,19),
4. ( 9,11,16,14)(10,13,15,12)( 1,17,41,40)( 4,20,44,37)( 6,22,46,35),
5. (17,19,24,22)(18,21,23,20)( 6,25,43,16)( 7,28,42,13)( 8,30,41,11),
6. (25,27,32,30)(26,29,31,28)( 3,38,43,19)( 5,36,45,21)( 8,33,48,24),
7. (33,35,40,38)(34,37,39,36)( 3, 9,46,32)( 2,12,47,29)( 1,14,48,27),
8. (41,43,48,46)(42,45,47,44)(14,22,30,38)(15,23,31,39)(16,24,32,40) );
9.
10. pamballbig:= Group(
11. (120,15)(20,55)(30,92)(1,14)(21,54)(31,93)(2,13)(22,53)(32,94)(3,12)(23,52)(33,95)(4,11)(24,51)(34,96)(5,10)(25,50)(47,106)(6,19)(26,59)(48,105)(7,18)(27,58)(49,104)(8,17)(28,57)(40,103)(9,16)(29,56)(41,102)
12. ,(60,75)(80,118)(42,101)(61,74)(81,119)(43,100)(62,73)(82,110)(44,109)(63,72)(83,111)(45,108)(64,71)(84,112)(46,107)(65,70)(85,113)(35,97)(66,79)(86,114)(36,98)(67,78)(87,115)(37,99)(68,77)(88,116)(38,90)(69,76)(89,117)(39,91)
13. ,(120,26)(10,39)(105,46)(1,27)(11,38)(104,47)(2,28)(12,37)(103,48)(3,29)(13,36)(102,49)(4,20)(14,35)(101,40)(5,21)(15,34)(112,58)(6,22)(16,33)(111,57)(7,23)(17,32)(110,56)(8,24)(18,31)(119,55)(9,25)(19,30)(118,54)
14. ,(60,89)(70,97)(117,53)(61,88)(71,96)(116,52)(62,87)(72,95)(115,51)(63,86)(73,94)(114,50)(64,85)(74,93)(113,59)(65,84)(75,92)(100,41)(66,83)(76,91)(109,42)(67,82)(77,90)(108,43)(68,81)(78,99)(107,44)(69,80)(79,98)(106,45)
15. ,(120,30)(20,46)(59,111)(1,31)(21,47)(58,110)(2,32)(22,48)(57,119)(3,33)(23,49)(56,118)(4,34)(24,40)(55,117)(5,35)(25,41)(10,74)(6,36)(26,42)(19,73)(7,37)(27,43)(18,72)(8,38)(28,44)(17,71)(9,39)(29,45)(16,70)
16. ,(60,96)(80,108)(15,79)(61,97)(81,109)(14,78)(62,98)(82,100)(13,77)(63,99)(83,101)(12,76)(64,90)(84,102)(11,75)(65,91)(85,103)(54,116)(66,92)(86,104)(53,115)(67,93)(87,105)(52,114)(68,94)(88,106)(51,113)(69,95)(89,107)(50,112)
17. ,(120,48)(30,59)(73,11)(1,49)(31,58)(72,10)(2,40)(32,57)(71,19)(3,41)(33,56)(70,18)(4,42)(34,55)(79,17)(5,43)(35,54)(86,29)(6,44)(36,53)(85,20)(7,45)(37,52)(84,21)(8,46)(38,51)(83,22)(9,47)(39,50)(82,23)
18. ,(60,103)(90,111)(81,24)(61,102)(91,110)(80,25)(62,101)(92,119)(89,26)(63,100)(93,118)(88,27)(64,109)(94,117)(87,28)(65,108)(95,116)(78,16)(66,107)(96,115)(77,15)(67,106)(97,114)(76,14)(68,105)(98,113)(75,13)(69,104)(99,112)(74,12)
19. ,(120,55)(10,49)(28,85)(1,54)(11,48)(29,84)(2,53)(12,47)(20,83)(3,52)(13,46)(21,82)(4,51)(14,45)(22,81)(5,50)(15,44)(31,91)(6,59)(16,43)(32,92)(7,58)(17,42)(33,93)(8,57)(18,41)(34,94)(9,56)(19,40)(35,95)
20. ,(60,111)(70,104)(36,96)(61,110)(71,105)(37,97)(62,119)(72,106)(38,98)(63,118)(73,107)(39,99)(64,117)(74,108)(30,90)(65,116)(75,109)(23,80)(66,115)(76,100)(24,89)(67,114)(77,101)(25,88)(68,113)(78,102)(26,87)(69,112)(79,103)(27,86)
21. ,(10,25)(120,109)(57,113)(11,24)(1,108)(56,112)(12,23)(2,107)(55,111)(13,22)(3,106)(54,110)(14,21)(4,105)(53,119)(15,20)(5,104)(93,39)(16,29)(6,103)(94,30)(17,28)(7,102)(95,31)(18,27)(8,101)(96,32)(19,26)(9,100)(97,33)
22. ,(70,88)(60,44)(34,98)(71,89)(61,45)(35,99)(72,80)(62,46)(36,90)(73,81)(63,47)(37,91)(74,82)(64,48)(38,92)(75,83)(65,49)(118,52)(76,84)(66,40)(117,51)(77,85)(67,41)(116,50)(78,86)(68,42)(115,59)(79,87)(69,43)(114,58)
23. ,(20,38)(120,113)(19,75)(21,39)(1,112)(18,74)(22,30)(2,111)(17,73)(23,31)(3,110)(16,72)(24,32)(4,119)(15,71)(25,33)(5,118)(104,45)(26,34)(6,117)(103,46)(27,35)(7,116)(102,47)(28,36)(8,115)(101,48)(29,37)(9,114)(100,49)
24. ,(80,91)(60,53)(40,119)(81,90)(61,52)(41,118)(82,99)(62,51)(42,117)(83,98)(63,50)(43,116)(84,97)(64,59)(44,115)(85,96)(65,58)(70,14)(86,95)(66,57)(79,13)(87,94)(67,56)(78,12)(88,93)(68,55)(77,11)(89,92)(69,54)(76,10)
25. ,(30,42)(120,73)(87,20)(31,43)(1,72)(86,21)(32,44)(2,71)(85,22)(33,45)(3,70)(84,23)(34,46)(4,79)(83,24)(35,47)(5,78)(50,110)(36,48)(6,77)(59,119)(37,49)(7,76)(58,118)(38,40)(8,75)(57,117)(39,41)(9,74)(56,116)
26. ,(90,103)(60,17)(55,115)(91,102)(61,16)(54,114)(92,101)(62,15)(53,113)(93,100)(63,14)(52,112)(94,109)(64,13)(51,111)(95,108)(65,12)(82,25)(96,107)(66,11)(81,26)(97,106)(67,10)(80,27)(98,105)(68,19)(89,28)(99,104)(69,18)(88,29)
27. ,(40,59)(120,83)(32,90)(41,58)(1,82)(33,91)(42,57)(2,81)(34,92)(43,56)(3,80)(35,93)(44,55)(4,89)(36,94)(45,54)(5,88)(72,12)(46,53)(6,87)(71,11)(47,52)(7,86)(70,10)(48,51)(8,85)(79,19)(49,50)(9,84)(78,18)
28. ,(100,112)(60,20)(77,17)(101,113)(61,21)(76,16)(102,114)(62,22)(75,15)(103,115)(63,23)(74,14)(104,116)(64,24)(73,13)(105,117)(65,25)(37,95)(106,118)(66,26)(38,96)(107,119)(67,27)(39,97)(108,110)(68,28)(30,98)(109,111)(69,29)(31,99)
29. ,(50,16)(120,96)(48,107)(51,17)(1,97)(49,106)(52,18)(2,98)(40,105)(53,19)(3,99)(41,104)(54,10)(4,90)(42,103)(55,11)(5,91)(84,27)(56,12)(6,92)(83,28)(57,13)(7,93)(82,29)(58,14)(8,94)(81,20)(59,15)(9,95)(80,21)
30. ,(110,78)(60,30)(22,89)(111,79)(61,31)(23,88)(112,70)(62,32)(24,87)(113,71)(63,33)(25,86)(114,72)(64,34)(26,85)(115,73)(65,35)(102,43)(116,74)(66,36)(101,44)(117,75)(67,37)(100,45)(118,76)(68,38)(109,46)(119,77)(69,39)(108,47)
31. ,(10,97)(50,102)(83,26)(11,96)(51,103)(82,27)(12,95)(52,104)(81,28)(13,94)(53,105)(80,29)(14,93)(54,106)(89,20)(15,92)(55,107)(61,5)(16,91)(56,108)(62,6)(17,90)(57,109)(63,7)(18,99)(58,100)(64,8)(19,98)(59,101)(65,9)
32. ,(10,100)(20,98)(62,4)(11,101)(21,99)(63,5)(12,102)(22,90)(64,6)(13,103)(23,91)(65,7)(14,104)(24,92)(66,8)(15,105)(25,93)(114,56)(16,106)(26,94)(113,55)(17,107)(27,95)(112,54)(18,108)(28,96)(111,53)(19,109)(29,97)(110,52)
33. ,(20,109)(10,116)(38,94)(21,108)(11,117)(39,95)(22,107)(12,118)(30,96)(23,106)(13,119)(31,97)(24,105)(14,110)(32,98)(25,104)(15,111)(3,63)(26,103)(16,112)(4,64)(27,102)(17,113)(5,65)(28,101)(18,114)(6,66)(29,100)(19,115)(7,67)
34. ,(110,25)(100,31)(2,64)(111,24)(101,30)(3,65)(112,23)(102,39)(4,66)(113,22)(103,38)(5,67)(114,21)(104,37)(6,68)(115,20)(105,36)(18,76)(116,29)(106,35)(17,75)(117,28)(107,34)(16,74)(118,27)(108,33)(15,73)(119,26)(109,32)(14,72)
35. ,(30,117)(20,77)(44,103)(31,116)(21,76)(45,102)(32,115)(22,75)(46,101)(33,114)(23,74)(47,100)(34,113)(24,73)(48,109)(35,112)(25,72)(1,65)(36,111)(26,71)(2,66)(37,110)(27,70)(3,67)(38,119)(28,79)(4,68)(39,118)(29,78)(5,69)
36. ,(30,79)(40,113)(66,120)(31,78)(41,112)(67,1)(32,77)(42,111)(68,2)(33,76)(43,110)(69,3)(34,75)(44,119)(60,4)(35,74)(45,118)(88,21)(36,73)(46,117)(87,22)(37,72)(47,116)(86,23)(38,71)(48,115)(85,24)(39,70)(49,114)(84,25)
37. ,(40,75)(30,81)(119,51)(41,74)(31,80)(118,50)(42,73)(32,89)(117,59)(43,72)(33,88)(116,58)(44,71)(34,87)(115,57)(45,70)(35,86)(67,9)(46,79)(36,85)(68,120)(47,78)(37,84)(69,1)(48,77)(38,83)(60,2)(49,76)(39,82)(61,3)
38. ,(40,87)(50,70)(8,68)(41,86)(51,71)(9,69)(42,85)(52,72)(120,60)(43,84)(53,73)(1,61)(44,83)(54,74)(2,62)(45,82)(55,75)(33,99)(46,81)(56,76)(34,90)(47,80)(57,77)(35,91)(48,89)(58,78)(36,92)(49,88)(59,79)(37,93)
39. ,(50,82)(40,90)(1,63)(51,83)(41,91)(120,62)(52,84)(42,92)(9,61)(53,85)(43,93)(8,60)(54,86)(44,94)(7,69)(55,87)(45,95)(19,77)(56,88)(46,96)(10,78)(57,89)(47,97)(11,79)(58,80)(48,98)(12,70)(59,81)(49,99)(13,71)
40. ,(50,95)(10,80)(6,60)(51,94)(11,81)(7,61)(52,93)(12,82)(8,62)(53,92)(13,83)(9,63)(54,91)(14,84)(120,64)(55,90)(15,85)(49,108)(56,99)(16,86)(40,107)(57,98)(17,87)(41,106)(58,97)(18,88)(42,105)(59,96)(19,89)(43,104)
41. );