Graph forms
for C4 [ 512, 522 ] = SS[512,45]
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On this page are computer-accessible forms for the graph C4[ 512, 522 ] =
SS[512,45].
(I) Following is a form readable by MAGMA:
g:=Graph<512|{ {22, 23}, {1, 3}, {1, 2}, {500, 503}, {1, 5}, {1, 4}, {370, 375},
{64, 69}, {18, 23}, {8, 14}, {497, 503}, {65, 71}, {64, 70}, {8, 15}, {88, 95},
{210, 213}, {66, 74}, {209, 217}, {48, 57}, {84, 93}, {65, 72}, {51, 58}, {50,
59}, {81, 91}, {498, 504}, {496, 506}, {369, 379}, {368, 378}, {87, 93}, {208,
218}, {6, 13}, {499, 504}, {66, 73}, {19, 24}, {7, 12}, {21, 25}, {83, 95}, {82,
94}, {22, 26}, {6, 11}, {464, 477}, {83, 94}, {49, 60}, {7, 10}, {20, 26}, {22,
24}, {22, 25}, {370, 381}, {369, 382}, {54, 57}, {53, 58}, {52, 59}, {39, 55},
{492, 508}, {489, 505}, {485, 501}, {453, 469}, {364, 380}, {360, 376}, {359,
375}, {356, 372}, {355, 371}, {75, 91}, {46, 62}, {205, 220}, {487, 502}, {463,
478}, {462, 479}, {459, 474}, {453, 468}, {363, 378}, {361, 376}, {206, 223},
{207, 222}, {47, 61}, {458, 472}, {451, 465}, {78, 92}, {197, 215}, {365, 382},
{490, 505}, {486, 501}, {366, 381}, {41, 61}, {495, 507}, {44, 56}, {6, 19},
{494, 507}, {460, 473}, {362, 383}, {45, 56}, {7, 18}, {200, 221}, {40, 62},
{455, 465}, {452, 466}, {42, 60}, {75, 92}, {493, 506}, {491, 508}, {454, 465},
{452, 467}, {451, 468}, {360, 383}, {355, 372}, {9, 17}, {366, 374}, {195, 219},
{204, 212}, {9, 16}, {459, 466}, {458, 467}, {34, 56}, {457, 467}, {367, 373},
{364, 374}, {38, 60}, {192, 218}, {193, 219}, {201, 211}, {33, 58}, {484, 511},
{455, 476}, {359, 380}, {37, 57}, {456, 468}, {357, 377}, {43, 55}, {196, 216},
{202, 214}, {8, 21}, {482, 511}, {454, 475}, {35, 62}, {32, 61}, {9, 20}, {194,
223}, {33, 63}, {488, 502}, {480, 510}, {460, 466}, {457, 471}, {456, 470},
{365, 371}, {32, 63}, {362, 373}, {358, 377}, {356, 379}, {36, 59}, {469, 501},
{477, 509}, {474, 506}, {470, 502}, {202, 235}, {479, 510}, {207, 238}, {209,
240}, {83, 113}, {473, 507}, {199, 229}, {475, 504}, {478, 509}, {75, 111},
{472, 508}, {77, 105}, {195, 231}, {203, 239}, {85, 112}, {193, 228}, {200,
237}, {198, 225}, {450, 485}, {449, 486}, {448, 487}, {199, 224}, {206, 233},
{30, 54}, {80, 120}, {71, 111}, {67, 107}, {31, 55}, {68, 109}, {79, 102}, {192,
233}, {194, 235}, {203, 226}, {30, 52}, {468, 510}, {68, 110}, {201, 227}, {30,
53}, {476, 503}, {463, 484}, {88, 115}, {76, 103}, {205, 230}, {77, 97}, {467,
511}, {465, 509}, {78, 98}, {196, 232}, {198, 234}, {28, 49}, {461, 480}, {84,
121}, {79, 98}, {76, 97}, {29, 48}, {28, 50}, {471, 505}, {90, 116}, {89, 119},
{28, 51}, {462, 481}, {461, 482}, {67, 108}, {85, 101}, {90, 106}, {27, 42},
{70, 119}, {29, 44}, {27, 41}, {71, 117}, {29, 47}, {27, 40}, {464, 483}, {89,
106}, {84, 103}, {80, 99}, {30, 45}, {29, 46}, {80, 100}, {79, 122}, {82, 100},
{86, 96}, {210, 228}, {28, 43}, {81, 102}, {197, 242}, {72, 112}, {77, 117},
{72, 113}, {89, 96}, {73, 115}, {86, 108}, {76, 118}, {73, 114}, {88, 99}, {27,
39}, {87, 107}, {78, 114}, {74, 118}, {69, 121}, {208, 236}, {85, 104}, {204,
241}, {70, 120}, {87, 105}, {86, 104}, {74, 116}, {69, 122}, {90, 101}, {82,
109}, {81, 110}, {179, 242}, {415, 478}, {414, 479}, {413, 479}, {304, 371},
{436, 496}, {306, 375}, {312, 381}, {161, 231}, {313, 383}, {314, 380}, {307,
372}, {444, 500}, {305, 379}, {443, 497}, {178, 249}, {309, 382}, {176, 252},
{446, 498}, {162, 239}, {175, 226}, {173, 224}, {172, 225}, {445, 499}, {190,
241}, {191, 240}, {163, 243}, {166, 246}, {164, 245}, {175, 254}, {165, 244},
{160, 242}, {179, 224}, {442, 489}, {441, 490}, {440, 491}, {180, 231}, {188,
239}, {172, 248}, {174, 250}, {183, 227}, {301, 377}, {170, 255}, {187, 238},
{303, 378}, {160, 246}, {173, 251}, {171, 253}, {161, 247}, {302, 376}, {182,
225}, {447, 488}, {186, 237}, {189, 234}, {438, 494}, {162, 251}, {187, 226},
{182, 236}, {437, 495}, {300, 374}, {439, 492}, {181, 232}, {184, 229}, {299,
373}, {435, 493}, {31, 64}, {168, 247}, {185, 230}, {149, 245}, {394, 490},
{158, 254}, {185, 217}, {35, 66}, {157, 252}, {34, 64}, {395, 489}, {393, 491},
{37, 65}, {392, 492}, {155, 255}, {184, 221}, {36, 66}, {156, 250}, {181, 211},
{38, 65}, {399, 488}, {386, 485}, {385, 486}, {384, 487}, {159, 248}, {154,
253}, {148, 243}, {191, 216}, {177, 217}, {153, 240}, {434, 475}, {432, 473},
{391, 494}, {390, 495}, {388, 493}, {188, 213}, {190, 215}, {178, 216}, {180,
222}, {183, 220}, {189, 214}, {152, 244}, {176, 220}, {156, 241}, {433, 476},
{186, 212}, {150, 249}, {131, 243}, {387, 499}, {163, 211}, {132, 245}, {424,
473}, {154, 232}, {425, 475}, {421, 471}, {420, 470}, {403, 481}, {167, 213},
{165, 215}, {57, 74}, {407, 484}, {133, 246}, {55, 67}, {171, 223}, {138, 254},
{136, 252}, {60, 73}, {431, 474}, {389, 496}, {174, 219}, {136, 253}, {61, 72},
{149, 227}, {430, 472}, {426, 476}, {419, 469}, {404, 482}, {152, 238}, {157,
234}, {406, 481}, {405, 482}, {402, 485}, {401, 486}, {400, 487}, {170, 221},
{148, 236}, {166, 222}, {159, 230}, {410, 483}, {397, 500}, {133, 255}, {429,
471}, {428, 470}, {409, 483}, {62, 69}, {411, 480}, {158, 229}, {63, 68}, {56,
68}, {417, 477}, {412, 480}, {408, 484}, {398, 498}, {168, 212}, {151, 235},
{135, 251}, {63, 67}, {58, 71}, {423, 474}, {396, 497}, {138, 247}, {137, 244},
{135, 250}, {59, 70}, {134, 248}, {427, 469}, {422, 472}, {416, 478}, {164,
218}, {147, 237}, {134, 249}, {418, 477}, {169, 214}, {155, 228}, {150, 233},
{47, 173}, {39, 163}, {45, 169}, {372, 497}, {44, 170}, {374, 496}, {46, 168},
{25, 145}, {380, 500}, {41, 161}, {26, 144}, {42, 160}, {40, 162}, {272, 410},
{274, 408}, {288, 426}, {25, 146}, {289, 426}, {290, 425}, {273, 413}, {382,
498}, {43, 166}, {381, 499}, {317, 434}, {318, 433}, {259, 403}, {378, 490},
{319, 431}, {315, 427}, {316, 428}, {263, 406}, {346, 459}, {340, 453}, {270,
415}, {54, 164}, {379, 489}, {377, 491}, {350, 460}, {344, 458}, {266, 409},
{345, 458}, {24, 140}, {349, 457}, {271, 411}, {24, 141}, {48, 165}, {26, 143},
{49, 167}, {376, 494}, {339, 453}, {317, 426}, {383, 488}, {348, 459}, {347,
460}, {319, 424}, {318, 425}, {40, 176}, {375, 495}, {373, 493}, {344, 448},
{260, 412}, {262, 414}, {23, 142}, {351, 454}, {53, 172}, {268, 405}, {269,
407}, {41, 178}, {42, 177}, {23, 139}, {50, 175}, {341, 456}, {51, 174}, {342,
456}, {343, 457}, {52, 171}, {371, 492}, {350, 449}, {349, 450}, {267, 404},
{315, 420}, {316, 419}, {293, 389}, {303, 399}, {300, 398}, {293, 390}, {291,
391}, {354, 454}, {297, 397}, {298, 398}, {49, 148}, {261, 416}, {298, 396},
{353, 455}, {291, 388}, {352, 455}, {296, 399}, {52, 156}, {265, 417}, {48,
153}, {51, 154}, {264, 418}, {297, 387}, {53, 158}, {50, 159}, {54, 155}, {292,
393}, {294, 395}, {292, 394}, {294, 392}, {276, 420}, {280, 424}, {277, 420},
{278, 423}, {311, 390}, {47, 157}, {256, 434}, {257, 434}, {258, 433}, {304,
387}, {39, 147}, {45, 152}, {295, 402}, {308, 386}, {310, 384}, {311, 385},
{295, 400}, {46, 150}, {44, 149}, {282, 419}, {287, 422}, {296, 401}, {299,
402}, {275, 425}, {307, 393}, {285, 422}, {286, 421}, {43, 151}, {281, 421},
{283, 423}, {301, 401}, {305, 397}, {313, 389}, {302, 400}, {306, 396}, {310,
392}, {314, 388}, {279, 424}, {284, 419}, {308, 395}, {309, 394}, {312, 391},
{327, 391}, {349, 413}, {335, 399}, {330, 394}, {331, 393}, {334, 396}, {338,
401}, {348, 415}, {339, 407}, {333, 392}, {350, 411}, {344, 414}, {346, 412},
{324, 387}, {337, 406}, {325, 398}, {338, 409}, {328, 388}, {351, 403}, {326,
395}, {340, 409}, {342, 408}, {329, 390}, {341, 410}, {336, 415}, {323, 402},
{325, 404}, {323, 407}, {353, 437}, {332, 408}, {328, 412}, {331, 414}, {354,
439}, {336, 389}, {335, 410}, {324, 403}, {330, 413}, {31, 199}, {31, 198},
{352, 442}, {334, 405}, {327, 411}, {337, 397}, {332, 400}, {348, 444}, {34,
195}, {82, 176}, {345, 443}, {78, 173}, {341, 438}, {33, 197}, {358, 386}, {298,
463}, {357, 384}, {346, 447}, {34, 196}, {347, 445}, {296, 462}, {77, 170},
{340, 435}, {326, 417}, {322, 421}, {321, 422}, {320, 423}, {37, 205}, {361,
385}, {89, 177}, {75, 163}, {38, 206}, {35, 202}, {343, 446}, {329, 416}, {292,
461}, {294, 463}, {38, 204}, {295, 461}, {79, 164}, {363, 384}, {351, 436},
{339, 440}, {35, 207}, {322, 430}, {321, 429}, {36, 200}, {36, 201}, {291, 462},
{37, 203}, {367, 385}, {333, 418}, {342, 441}, {32, 208}, {320, 432}, {33, 209},
{32, 210}, {368, 386}, {84, 167}, {88, 172}, {90, 174}, {80, 165}, {352, 405},
{83, 166}, {293, 464}, {343, 417}, {354, 404}, {353, 406}, {297, 464}, {345,
418}, {347, 416}, {85, 169}, {87, 171}, {76, 178}, {86, 168}, {81, 175}, {92,
349}, {110, 367}, {108, 365}, {113, 370}, {95, 346}, {117, 368}, {109, 363},
{103, 352}, {104, 353}, {93, 343}, {94, 340}, {105, 354}, {122, 369}, {107,
359}, {111, 355}, {91, 342}, {116, 356}, {120, 364}, {115, 358}, {118, 366},
{112, 362}, {114, 360}, {121, 357}, {220, 448}, {119, 361}, {12, 301}, {227,
450}, {225, 450}, {226, 449}, {10, 302}, {10, 303}, {17, 311}, {11, 300}, {12,
299}, {16, 313}, {17, 312}, {16, 314}, {123, 337}, {236, 448}, {11, 315}, {125,
333}, {124, 332}, {19, 291}, {12, 317}, {98, 339}, {14, 319}, {13, 316}, {20,
295}, {242, 449}, {10, 318}, {127, 331}, {18, 294}, {106, 351}, {99, 341}, {127,
329}, {126, 328}, {18, 293}, {19, 292}, {14, 310}, {126, 326}, {124, 324}, {123,
323}, {97, 345}, {15, 309}, {125, 327}, {100, 350}, {11, 304}, {15, 308}, {13,
305}, {96, 348}, {21, 297}, {14, 307}, {21, 296}, {20, 298}, {102, 344}, {101,
347}, {13, 306}, {241, 437}, {247, 432}, {248, 432}, {240, 444}, {95, 274},
{255, 433}, {15, 320}, {17, 321}, {94, 270}, {113, 288}, {238, 447}, {16, 322},
{91, 265}, {232, 442}, {231, 436}, {252, 431}, {253, 430}, {254, 429}, {249,
429}, {230, 435}, {250, 431}, {251, 430}, {92, 266}, {235, 445}, {237, 443},
{239, 441}, {243, 427}, {245, 428}, {120, 290}, {228, 446}, {246, 428}, {122,
289}, {234, 438}, {124, 289}, {229, 440}, {93, 259}, {233, 439}, {224, 447},
{244, 427}, {124, 284}, {218, 442}, {219, 443}, {117, 276}, {126, 287}, {118,
279}, {119, 277}, {121, 282}, {125, 286}, {215, 436}, {223, 444}, {127, 283},
{211, 439}, {221, 441}, {214, 435}, {216, 445}, {97, 263}, {127, 281}, {99,
261}, {104, 271}, {123, 275}, {100, 269}, {126, 279}, {116, 285}, {114, 283},
{98, 264}, {212, 446}, {125, 278}, {222, 437}, {96, 268}, {112, 284}, {115,
286}, {213, 440}, {101, 267}, {123, 277}, {106, 260}, {105, 262}, {217, 438},
{109, 287}, {108, 281}, {102, 272}, {110, 280}, {103, 273}, {111, 275}, {107,
278}, {141, 269}, {144, 273}, {131, 256}, {189, 313}, {190, 314}, {142, 267},
{132, 258}, {181, 307}, {139, 268}, {143, 264}, {141, 266}, {137, 257}, {143,
262}, {186, 304}, {188, 310}, {139, 263}, {180, 312}, {184, 308}, {142, 259},
{185, 311}, {187, 299}, {147, 257}, {191, 300}, {129, 276}, {151, 258}, {145,
260}, {146, 261}, {128, 280}, {130, 282}, {183, 303}, {144, 265}, {153, 256},
{182, 301}, {140, 272}, {128, 285}, {146, 271}, {179, 302}, {140, 274}, {145,
270}, {130, 288}, {129, 290}, {167, 257}, {169, 256}, {188, 272}, {189, 274},
{141, 317}, {143, 319}, {140, 318}, {181, 263}, {184, 266}, {190, 268}, {177,
258}, {185, 269}, {142, 315}, {187, 270}, {179, 261}, {139, 316}, {191, 260},
{186, 262}, {182, 264}, {183, 265}, {180, 267}, {135, 327}, {132, 325}, {136,
329}, {135, 326}, {133, 324}, {6, 452}, {138, 328}, {136, 330}, {7, 452}, {192,
259}, {208, 275}, {137, 332}, {161, 356}, {133, 323}, {210, 276}, {130, 325},
{138, 333}, {9, 451}, {128, 330}, {8, 451}, {131, 335}, {160, 364}, {130, 335},
{162, 367}, {134, 331}, {131, 334}, {194, 271}, {209, 284}, {129, 334}, {128,
336}, {144, 320}, {193, 273}, {203, 283}, {204, 285}, {196, 278}, {200, 282},
{129, 338}, {146, 321}, {145, 322}, {205, 286}, {132, 338}, {134, 336}, {137,
337}, {198, 287}, {206, 279}, {195, 281}, {199, 280}, {202, 277}, {147, 368},
{148, 369}, {197, 288}, {201, 289}, {152, 370}, {207, 290}, {153, 361}, {193,
305}, {194, 306}, {150, 359}, {156, 365}, {2, 502}, {159, 363}, {154, 366}, {3,
503}, {192, 309}, {149, 355}, {158, 360}, {2, 501}, {4, 508}, {5, 511}, {3,
504}, {157, 358}, {3, 510}, {151, 362}, {4, 505}, {5, 507}, {155, 357}, {2,
509}, {5, 506}, {4, 512}, {466, 512}, {481, 512}, {483, 512} }>;
(II) A more general form is to represent the graph as the orbit of {22, 23}
under the group generated by the following permutations:
a: (1, 10, 185, 415, 461, 401, 99, 16)(2, 302, 311, 478, 295, 486, 261, 9)(3,
303, 217, 336, 482, 301, 80, 322)(4, 318, 230, 348, 292, 338, 88, 314)(5, 7,
269, 270, 480, 296, 341, 313)(6, 266, 83, 328, 481, 272, 214, 474)(8, 470, 360,
495, 294, 323, 226, 271)(11, 92, 113, 126, 403, 102, 169, 431)(12, 100, 145,
510, 399, 438, 389, 511)(13, 184, 166, 138, 406, 188, 202, 423)(14, 420, 114,
375, 395, 133, 175, 104)(15, 428, 158, 437, 392, 123, 203, 194)(17, 509, 400,
385, 416, 20, 501, 179)(18, 407, 187, 411, 21, 456, 383, 507)(19, 409, 95, 388,
512, 140, 435, 459)(22, 453, 447, 391, 464, 408, 373, 460)(23, 339, 238, 327,
297, 342, 362, 473)(24, 340, 346, 291, 483, 274, 493, 466)(25, 468, 488, 494,
293, 484, 299, 350)(26, 469, 224, 312, 477, 332, 367, 347)(27, 178, 103, 121,
64, 195, 443, 147)(28, 168, 181, 210, 66, 107, 379, 170)(29, 154, 446, 201, 63,
116, 105, 148)(30, 156, 371, 111, 65, 206, 192, 164)(31, 231, 345, 257, 40, 216,
273, 282)(32, 74, 87, 369, 44, 51, 212, 211)(33, 285, 354, 236, 48, 253, 498,
227)(34, 219, 237, 39, 41, 76, 84, 69)(35, 278, 305, 221, 43, 247, 263, 213)(36,
67, 356, 77, 49, 46, 232, 228)(37, 223, 309, 245, 53, 241, 492, 275)(38, 233,
218, 54, 52, 365, 355, 71)(42, 249, 352, 357, 70, 281, 497, 368)(45, 250, 304,
75, 72, 279, 259, 79)(47, 366, 343, 289, 68, 90, 262, 243)(50, 86, 307, 276, 73,
359, 489, 255)(55, 161, 97, 167, 62, 196, 193, 200)(56, 174, 186, 163, 61, 118,
93, 122)(57, 171, 382, 149, 58, 204, 439, 208)(59, 108, 372, 117, 60, 150, 442,
155)(78, 370, 326, 324, 81, 85, 319, 315)(82, 260, 479, 335, 234, 496, 467,
317)(89, 331, 334, 358, 364, 471, 476, 363)(91, 112, 424, 142, 98, 152, 135,
387)(94, 412, 462, 410, 189, 506, 452, 141)(96, 393, 129, 115, 380, 505, 433,
159)(101, 143, 427, 173, 381, 417, 124, 110)(106, 414, 131, 157, 374, 457, 426,
109)(119, 127, 396, 386, 160, 429, 455, 384)(120, 421, 503, 378, 177, 134, 405,
377)(125, 397, 441, 151, 432, 139, 440, 207)(128, 404, 182, 165, 430, 504, 183,
209)(130, 198, 436, 458, 434, 176, 191, 413)(132, 172, 190, 508, 425, 205, 444,
394)(136, 398, 450, 197, 422, 454, 448, 153)(137, 162, 445, 144, 419, 199, 180,
418)(146, 451, 502, 376, 390, 463, 402, 449)(215, 472, 475, 220, 240, 330, 325,
225)(222, 333, 337, 239, 235, 320, 316, 229)(242, 321, 465, 487, 361, 329, 298,
485)(244, 251, 499, 265, 284, 280, 267, 264)(246, 254, 353, 310, 277, 283, 306,
308)(248, 268, 491, 290, 286, 500, 490, 258)(252, 300, 349, 288, 287, 351, 344,
256) (III) Last is Groups&Graphs. Copy everything between (not including)
the lines of asterisks into a plain text file and save it as "graph.txt". Then
launch G&G (Groups&Graphs) and select Read Text from the File menu.
**************
&Graph **************
b: (2, 5, 3, 4)(6, 8, 7, 9)(10, 17, 11, 14)(12, 16, 13, 15)(18, 20, 19, 21)(23,
26, 24, 25)(28, 29)(31, 35, 38, 32)(33, 34, 36, 37)(39, 40, 42, 41)(43, 46, 49,
47)(44, 50, 48, 51)(45, 52, 54, 53)(55, 62, 60, 61)(56, 59, 57, 58)(63, 64, 66,
65)(67, 69, 73, 72)(68, 70, 74, 71)(75, 82, 89, 76)(77, 81, 80, 90)(78, 83, 86,
84)(79, 88, 85, 87)(91, 100, 106, 97)(92, 94, 96, 103)(93, 98, 95, 104)(99, 101,
105, 102)(107, 122, 115, 112)(108, 121, 114, 113)(109, 119, 118, 111)(110, 120,
116, 117)(123, 126)(124, 125)(127, 130)(128, 129)(131, 136, 132, 134)(133, 138,
137, 135)(139, 144, 141, 145)(140, 146, 142, 143)(147, 162, 160, 161)(148, 157,
151, 150)(149, 159, 153, 154)(152, 156, 155, 158)(163, 176, 177, 178)(164, 172,
169, 171)(165, 174, 170, 175)(166, 168, 167, 173)(179, 180, 186, 188)(181, 183,
185, 191)(182, 189, 194, 192)(184, 187, 190, 193)(195, 200, 203, 197)(196, 201,
205, 209)(198, 202, 206, 208)(199, 207, 204, 210)(211, 220, 217, 216)(212, 213,
224, 222)(214, 223, 218, 225)(215, 219, 221, 226)(227, 230, 240, 232)(228, 229,
238, 241)(231, 237, 239, 242)(233, 236, 234, 235)(243, 252, 258, 249)(244, 250,
255, 254)(245, 248, 256, 253)(246, 247, 257, 251)(259, 264, 274, 271)(260, 263,
265, 269)(261, 267, 262, 272)(266, 270, 268, 273)(275, 287, 277, 279)(276, 280,
290, 285)(278, 289, 286, 284)(281, 282, 283, 288)(291, 297, 294, 295)(292, 296,
293, 298)(299, 314, 305, 308)(300, 307, 303, 311)(301, 313, 306, 309)(302, 312,
304, 310)(315, 319, 318, 321)(316, 320, 317, 322)(323, 328, 337, 326)(324, 333,
332, 327)(325, 331, 335, 329)(330, 338, 336, 334)(339, 346, 353, 343)(340, 348,
352, 349)(341, 347, 354, 344)(342, 350, 351, 345)(355, 363, 361, 366)(356, 368,
367, 364)(357, 360, 370, 365)(358, 362, 359, 369)(371, 384, 376, 381)(372, 378,
385, 374)(373, 380, 379, 386)(375, 382, 377, 383)(387, 392, 400, 391)(388, 397,
395, 402)(389, 396, 394, 401)(390, 398, 393, 399)(403, 418, 408, 411)(404, 414,
410, 416)(405, 413, 409, 415)(406, 417, 407, 412)(419, 423, 426, 421)(420, 424,
425, 422)(427, 431, 433, 429)(428, 432, 434, 430)(435, 444, 442, 450)(436, 443,
441, 449)(437, 446, 440, 447)(438, 445, 439, 448)(451, 452)(453, 459, 455,
457)(454, 458, 456, 460)(461, 462, 464, 463)(465, 467, 468, 466)(469, 474, 476,
471)(470, 473, 475, 472)(477, 484, 480, 481)(478, 482, 479, 483)(485, 493, 500,
489)(486, 496, 497, 490)(487, 494, 499, 492)(488, 495, 498, 491)(501, 506, 503,
505)(502, 507, 504, 508)(509, 511, 510, 512)
c: (4, 5)(8, 9)(10, 12)(11, 13)(14, 17)(15, 16)(20, 21)(25, 26)(27, 28)(29,
30)(32, 33)(35, 36)(39, 43)(40, 50)(41, 51)(42, 49)(44, 45)(46, 52)(47, 53)(48,
54)(58, 61)(59, 62)(69, 70)(71, 72)(75, 83)(76, 90)(77, 85)(78, 88)(79, 80)(81,
82)(84, 89)(86, 87)(91, 94)(92, 95)(93, 96)(97, 101)(98, 99)(100, 102)(103,
106)(104, 105)(107, 108)(109, 110)(111, 113)(112, 117)(114, 115)(116, 118)(119,
121)(120, 122)(123, 130)(124, 129)(125, 127)(126, 128)(131, 133)(132, 137)(134,
135)(136, 138)(139, 142)(140, 141)(143, 146)(144, 145)(147, 151)(148, 160)(149,
152)(150, 156)(153, 155)(154, 161)(157, 158)(159, 162)(163, 166)(164, 165)(167,
177)(168, 171)(169, 170)(172, 173)(174, 178)(175, 176)(179, 182)(180, 181)(183,
187)(184, 189)(185, 188)(186, 194)(190, 192)(191, 193)(195, 196)(197, 208)(198,
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