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On this page are computer-accessible forms for the graph C4[ 216, 40 ] = UG(ATD[216,15]).

(I) Following is a form readable by MAGMA:

g:=Graph<216|{ {28, 29}, {76, 78}, {173, 175}, {136, 138}, {1, 2}, {25, 26}, {1, 5}, {64, 68}, {3, 7}, {2, 6}, {105, 108}, {128, 135}, {81, 89}, {150, 158}, {149, 157}, {114, 123}, {69, 78}, {2, 14}, {68, 72}, {4, 8}, {3, 15}, {115, 127}, {113, 124}, {177, 188}, {23, 24}, {47, 62}, {168, 185}, {96, 113}, {103, 116}, {165, 182}, {163, 176}, {139, 152}, {4, 16}, {13, 25}, {12, 24}, {7, 19}, {6, 18}, {5, 17}, {164, 177}, {197, 208}, {165, 179}, {163, 180}, {173, 186}, {37, 61}, {205, 213}, {203, 211}, {175, 183}, {138, 146}, {200, 210}, {132, 159}, {204, 215}, {202, 209}, {8, 20}, {171, 183}, {11, 23}, {10, 22}, {9, 21}, {76, 80}, {175, 178}, {68, 90}, {204, 210}, {160, 190}, {46, 49}, {29, 61}, {31, 63}, {30, 62}, {24, 57}, {26, 59}, {4, 38}, {157, 191}, {72, 106}, {21, 55}, {20, 54}, {17, 51}, {16, 50}, {13, 47}, {12, 46}, {9, 43}, {8, 42}, {5, 39}, {25, 58}, {75, 104}, {89, 122}, {139, 174}, {10, 44}, {19, 53}, {18, 52}, {11, 45}, {138, 172}, {27, 60}, {145, 185}, {147, 187}, {28, 55}, {147, 184}, {94, 114}, {153, 181}, {6, 40}, {22, 56}, {7, 41}, {73, 121}, {154, 168}, {86, 101}, {9, 61}, {143, 187}, {140, 184}, {13, 57}, {11, 63}, {10, 60}, {12, 58}, {7, 48}, {154, 173}, {20, 35}, {92, 107}, {78, 118}, {70, 127}, {76, 117}, {137, 179}, {64, 124}, {14, 48}, {67, 125}, {15, 49}, {88, 103}, {159, 160}, {142, 206}, {153, 216}, {56, 122}, {146, 208}, {32, 99}, {149, 214}, {61, 126}, {50, 118}, {145, 213}, {144, 212}, {63, 123}, {51, 119}, {136, 204}, {17, 84}, {140, 201}, {37, 96}, {130, 199}, {28, 90}, {150, 208}, {41, 111}, {40, 110}, {37, 98}, {147, 212}, {144, 215}, {48, 119}, {41, 110}, {131, 203}, {156, 212}, {139, 195}, {141, 196}, {33, 107}, {38, 109}, {142, 197}, {18, 94}, {142, 194}, {53, 121}, {52, 120}, {19, 95}, {15, 66}, {16, 93}, {34, 108}, {142, 192}, {30, 78}, {25, 72}, {155, 202}, {151, 198}, {149, 196}, {11, 89}, {151, 197}, {145, 195}, {15, 92}, {14, 91}, {156, 201}, {152, 205}, {147, 198}, {145, 199}, {36, 124}, {153, 193}, {42, 112}, {47, 117}, {46, 116}, {43, 113}, {33, 125}, {155, 199}, {32, 125}, {35, 126}, {34, 127}, {44, 114}, {45, 115}, {30, 65}, {31, 127}, {171, 203}, {34, 66}, {33, 65}, {32, 64}, {27, 122}, {38, 71}, {58, 88}, {168, 202}, {48, 83}, {187, 216}, {39, 66}, {22, 112}, {164, 194}, {36, 67}, {176, 215}, {42, 77}, {57, 81}, {162, 203}, {59, 80}, {163, 200}, {186, 214}, {2, 111}, {167, 202}, {38, 75}, {161, 207}, {56, 87}, {166, 201}, {57, 86}, {36, 84}, {54, 71}, {162, 209}, {181, 198}, {20, 96}, {172, 216}, {167, 211}, {23, 99}, {22, 98}, {21, 97}, {29, 104}, {31, 106}, {52, 66}, {182, 192}, {30, 105}, {54, 65}, {49, 70}, {174, 214}, {1, 120}, {55, 77}, {21, 110}, {59, 64}, {28, 103}, {24, 100}, {35, 95}, {27, 102}, {62, 67}, {169, 215}, {26, 101}, {40, 87}, {39, 166}, {5, 129}, {10, 130}, {47, 167}, {46, 166}, {45, 165}, {44, 164}, {43, 163}, {42, 162}, {41, 161}, {40, 160}, {12, 132}, {53, 188}, {59, 178}, {88, 209}, {26, 144}, {62, 181}, {69, 206}, {93, 208}, {4, 138}, {13, 131}, {90, 213}, {58, 171}, {56, 170}, {65, 211}, {8, 155}, {86, 193}, {32, 184}, {87, 207}, {9, 144}, {6, 156}, {83, 207}, {54, 168}, {55, 169}, {77, 210}, {89, 198}, {91, 196}, {17, 176}, {53, 148}, {97, 195}, {108, 206}, {19, 183}, {31, 185}, {50, 148}, {106, 205}, {124, 212}, {29, 180}, {102, 207}, {113, 216}, {44, 134}, {60, 151}, {126, 213}, {101, 201}, {43, 133}, {23, 167}, {60, 143}, {51, 135}, {117, 193}, {100, 209}, {63, 137}, {118, 192}, {39, 159}, {52, 140}, {117, 204}, {14, 180}, {36, 158}, {104, 210}, {122, 193}, {33, 157}, {34, 158}, {123, 199}, {3, 189}, {109, 211}, {1, 190}, {119, 200}, {71, 134}, {111, 174}, {121, 189}, {123, 191}, {101, 160}, {83, 148}, {73, 128}, {91, 146}, {116, 189}, {119, 190}, {73, 131}, {74, 129}, {76, 135}, {74, 135}, {79, 130}, {74, 132}, {81, 159}, {93, 141}, {102, 182}, {84, 133}, {94, 143}, {107, 186}, {109, 188}, {16, 194}, {71, 149}, {106, 184}, {69, 150}, {80, 131}, {85, 134}, {94, 141}, {3, 214}, {116, 161}, {82, 132}, {99, 181}, {18, 197}, {102, 190}, {27, 194}, {98, 187}, {99, 185}, {105, 179}, {82, 137}, {93, 134}, {92, 129}, {91, 133}, {75, 148}, {104, 183}, {80, 176}, {111, 141}, {45, 206}, {82, 177}, {115, 151}, {126, 154}, {79, 170}, {95, 186}, {37, 195}, {73, 175}, {84, 178}, {85, 179}, {100, 130}, {35, 196}, {77, 170}, {81, 182}, {125, 154}, {70, 174}, {68, 173}, {69, 172}, {75, 162}, {85, 188}, {105, 128}, {112, 153}, {85, 191}, {95, 180}, {100, 137}, {109, 128}, {72, 166}, {79, 161}, {92, 178}, {97, 143}, {120, 150}, {67, 172}, {74, 165}, {82, 189}, {90, 171}, {108, 157}, {88, 170}, {96, 146}, {51, 192}, {107, 158}, {110, 152}, {83, 164}, {112, 136}, {121, 129}, {70, 191}, {98, 155}, {114, 139}, {50, 200}, {49, 205}, {97, 156}, {120, 133}, {79, 177}, {87, 169}, {118, 136}, {86, 169}, {103, 152}, {115, 140} }>;

(II) A more general form is to represent the graph as the orbit of {28, 29} under the group generated by the following permutations:

a: (2, 5)(4, 11)(6, 17)(7, 15)(8, 23)(9, 26)(10, 30)(12, 35)(13, 37)(14, 39)(16, 45)(18, 51)(19, 49)(20, 24)(21, 59)(22, 62)(25, 61)(27, 69)(28, 68)(29, 72)(31, 75)(32, 77)(33, 79)(34, 83)(36, 87)(38, 63)(40, 84)(41, 92)(42, 99)(43, 101)(44, 105)(46, 95)(47, 98)(48, 66)(50, 115)(52, 119)(53, 70)(54, 100)(55, 64)(56, 67)(57, 96)(58, 126)(60, 78)(65, 130)(71, 137)(73, 139)(74, 141)(76, 143)(80, 97)(81, 146)(82, 149)(86, 113)(88, 154)(89, 138)(91, 159)(93, 165)(94, 135)(102, 150)(103, 173)(104, 106)(107, 161)(108, 164)(109, 123)(110, 178)(111, 129)(112, 181)(114, 128)(116, 186)(117, 187)(118, 151)(120, 190)(121, 174)(122, 172)(124, 169)(125, 170)(127, 148)(131, 195)(132, 196)(133, 160)(134, 179)(136, 198)(140, 200)(145, 203)(147, 204)(152, 175)(155, 167)(156, 176)(157, 177)(158, 207)(162, 185)(163, 201)(166, 180)(168, 209)(171, 213)(182, 208)(183, 205)(184, 210)(188, 191)(189, 214)(192, 197)(193, 216)(194, 206)(199, 211)(212, 215)
b: (1, 2, 6, 18, 52, 120)(3, 9, 27, 70, 124, 192)(4, 12, 20, 57, 71, 25)(5, 14, 40, 94, 140, 150)(7, 21, 60, 127, 36, 51)(8, 24, 54, 13, 38, 58)(10, 31, 67, 135, 19, 55)(11, 33, 80, 148, 103, 98)(15, 43, 102, 174, 212, 142)(16, 46, 96, 81, 149, 26)(17, 48, 110, 143, 115, 158)(22, 63, 125, 76, 53, 28)(23, 65, 131, 75, 88, 155)(29, 56, 123, 32, 78, 121)(30, 73, 104, 170, 199, 99)(34, 84, 119, 41, 97, 151)(35, 86, 134, 72, 138, 132)(37, 89, 157, 59, 50, 116)(39, 91, 160, 141, 201, 208)(42, 100, 168, 47, 109, 171)(44, 106, 172, 74, 95, 169)(45, 107, 176, 83, 152, 187)(49, 113, 182, 214, 144, 194)(61, 122, 191, 64, 118, 189)(62, 128, 183, 77, 130, 185)(66, 133, 190, 111, 156, 197)(68, 136, 82, 126, 193, 85)(69, 129, 180, 87, 114, 184)(79, 145, 181, 105, 175, 210)(90, 112, 137, 154, 117, 188)(92, 163, 207, 139, 147, 206)(93, 166, 146, 159, 196, 101)(108, 178, 200, 161, 195, 198)(153, 179, 173, 204, 177, 213)(162, 209, 202, 167, 211, 203)(164, 205, 216, 165, 186, 215)

(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.

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&Graph
C4[ 216, 40 ]
216
-1 2 190 5 120
-2 1 111 14 6
-3 189 15 214 7
-4 16 38 138 8
-5 1 17 39 129
-6 2 156 18 40
-7 3 48 19 41
-8 155 4 20 42
-9 144 61 21 43
-10 22 44 60 130
-11 23 45 89 63
-12 132 24 46 58
-13 57 25 47 131
-14 2 91 48 180
-15 66 3 92 49
-16 4 93 50 194
-17 176 5 51 84
-18 6 94 52 197
-19 7 95 183 53
-20 35 8 96 54
-21 55 110 9 97
-22 56 112 10 98
-23 11 99 24 167
-24 12 23 100 57
-25 13 58 26 72
-26 144 101 25 59
-27 122 102 60 194
-28 55 90 103 29
-29 180 104 28 61
-30 78 105 62 65
-31 127 106 63 185
-32 99 125 184 64
-33 157 125 107 65
-34 66 158 127 108
-35 126 95 20 196
-36 67 124 158 84
-37 61 96 195 98
-38 4 71 75 109
-39 66 166 5 159
-40 110 6 160 87
-41 110 111 7 161
-42 77 112 8 162
-43 133 113 9 163
-44 134 114 10 164
-45 11 165 115 206
-46 12 166 49 116
-47 13 167 62 117
-48 14 83 7 119
-49 46 15 70 205
-50 200 16 148 118
-51 135 192 17 119
-52 66 18 140 120
-53 121 188 148 19
-54 168 71 20 65
-55 77 169 28 21
-56 22 122 170 87
-57 13 24 81 86
-58 88 12 25 171
-59 178 80 26 64
-60 143 27 151 10
-61 37 126 29 9
-62 67 47 181 30
-63 11 123 137 31
-64 68 124 59 32
-65 33 211 30 54
-66 34 15 39 52
-67 36 125 62 172
-68 90 72 173 64
-69 78 150 172 206
-70 191 49 127 174
-71 134 38 149 54
-72 166 68 25 106
-73 121 128 131 175
-74 132 165 135 129
-75 38 104 148 162
-76 78 80 135 117
-77 55 210 170 42
-78 69 30 118 76
-79 177 170 161 130
-80 176 59 76 131
-81 89 57 159 182
-82 132 177 189 137
-83 48 148 207 164
-84 133 178 36 17
-85 188 134 179 191
-86 57 101 169 193
-87 56 169 40 207
-88 209 58 103 170
-89 11 198 122 81
-90 68 213 28 171
-91 133 14 146 196
-92 178 15 107 129
-93 134 16 141 208
-94 143 114 18 141
-95 35 180 19 186
-96 113 146 37 20
-97 143 156 195 21
-98 22 187 155 37
-99 23 181 185 32
-100 209 24 137 130
-101 201 26 160 86
-102 190 27 182 207
-103 88 28 116 152
-104 210 29 183 75
-105 179 128 30 108
-106 72 205 184 31
-107 33 92 158 186
-108 34 157 105 206
-109 188 211 38 128
-110 40 41 152 21
-111 2 41 141 174
-112 22 136 42 153
-113 124 216 96 43
-114 44 123 94 139
-115 45 127 140 151
-116 46 189 103 161
-117 47 193 204 76
-118 78 136 192 50
-119 200 190 48 51
-120 1 133 150 52
-121 189 73 129 53
-122 56 89 27 193
-123 199 114 191 63
-124 36 113 212 64
-125 33 154 67 32
-126 154 35 213 61
-127 34 70 115 31
-128 135 105 73 109
-129 121 92 5 74
-130 100 199 79 10
-131 13 80 203 73
-132 12 82 159 74
-133 91 84 43 120
-134 44 71 93 85
-135 51 128 74 76
-136 112 138 204 118
-137 100 179 82 63
-138 146 4 136 172
-139 114 195 152 174
-140 201 115 52 184
-141 111 93 94 196
-142 192 194 206 197
-143 187 60 94 97
-144 212 26 215 9
-145 199 213 195 185
-146 91 138 96 208
-147 187 198 212 184
-148 50 83 53 75
-149 157 71 214 196
-150 69 158 120 208
-151 198 60 115 197
-152 110 103 139 205
-153 112 181 193 216
-154 168 125 126 173
-155 199 202 8 98
-156 201 212 6 97
-157 33 191 149 108
-158 34 36 150 107
-159 132 81 39 160
-160 101 190 159 40
-161 79 116 41 207
-162 209 203 42 75
-163 176 200 180 43
-164 44 177 83 194
-165 45 179 182 74
-166 46 201 39 72
-167 23 211 47 202
-168 154 202 185 54
-169 55 215 86 87
-170 77 88 56 79
-171 90 58 203 183
-172 67 69 138 216
-173 154 68 175 186
-174 111 70 214 139
-175 178 73 183 173
-176 80 17 215 163
-177 188 79 82 164
-178 59 92 84 175
-179 165 137 105 85
-180 14 29 95 163
-181 99 198 62 153
-182 165 102 81 192
-183 104 171 19 175
-184 147 106 140 32
-185 99 145 168 31
-186 214 95 107 173
-187 143 147 216 98
-188 177 85 53 109
-189 121 3 82 116
-190 1 102 160 119
-191 123 157 70 85
-192 182 51 118 142
-193 122 117 86 153
-194 16 27 142 164
-195 145 37 139 97
-196 35 91 149 141
-197 18 151 142 208
-198 89 147 181 151
-199 155 123 145 130
-200 210 50 119 163
-201 166 101 156 140
-202 209 155 167 168
-203 211 171 162 131
-204 210 136 215 117
-205 213 49 106 152
-206 45 69 108 142
-207 102 83 161 87
-208 146 93 150 197
-209 88 100 202 162
-210 77 200 104 204
-211 167 203 65 109
-212 144 156 124 147
-213 90 145 126 205
-214 3 149 174 186
-215 176 144 169 204
-216 187 113 172 153
0

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