# -*- GAP -*-

d6p_pencil :=
rec(
  graph := [ rec(
          adjacencies := [ [ 7 ], [ 7 ], [ 5 ], [ 5 ], [ 3, 4, 6 ], [ 5, 7 ], [ 1, 2, 6 ], [ 14 ], [ 14 ], [ 12 ], 
              [ 12 ], [ 10, 11, 13 ], [ 12, 14 ], [ 8, 9, 13 ], [ 21 ], [ 21 ], [ 19 ], [ 19 ], [ 17, 18, 20 ], 
              [ 19, 21 ], [ 15, 16, 20 ] ],
          autGroup := Group( [ (17,18), (15,16), (15,17)(16,18)(19,21), (10,11), ( 8, 9), ( 8,10)( 9,11)(12,14), 
              ( 8,15)( 9,16)(10,17)(11,18)(12,19)(13,20)(14,21), ( 3, 4), ( 1, 2), ( 1, 3)( 2, 4)( 5, 7), 
              ( 1, 8)( 2, 9)( 3,10)( 4,11)( 5,12)( 6,13)( 7,14) ] ),
          forms := [ rec(
                  forms := [ [ "[20, 0, 20]" ], [ "[4, 0, 4]" ] ],
                  h := 220 ), rec(
                  forms := [ [ "[4, 0, 100]" ] ],
                  h := 224 ), rec(
                  forms := [ [ "[8, 4, 52]" ] ],
                  h := 228 ), rec(
                  forms := [ [ "[8, 4, 52]" ] ],
                  h := 232 ), rec(
                  forms := [ [ "[4, 0, 100]" ] ],
                  h := 236 ) ],
          group := Group( [ () ] ),
          h := [ 220, 224, 228, 232, 236 ],
          info := rec(
              bipartite := true,
              distance_regular := false,
              girth := -1,
              pencils := [ [ 3, 6 ], [ 2, 3 ], [ 1, 12 ] ],
              regular := false,
              transitive := -1 ),
          isGraph := true,
          isSimple := true,
          names := [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21 ],
          order := 21,
          real := [  ],
          representatives := [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21 ],
          schreierVector := [ -1, -2, -3, -4, -5, -6, -7, -8, -9, -10, -11, -12, -13, -14, -15, -16, -17, -18, -19, 
              -20, -21 ] ), rec(
          adjacencies := [ [ 7 ], [ 7 ], [ 5 ], [ 5 ], [ 3, 4, 6 ], [ 5, 7 ], [ 1, 2, 6 ], [ 14 ], [ 14 ], [ 12 ], 
              [ 12 ], [ 10, 11, 13 ], [ 12, 14 ], [ 8, 9, 13 ], [ 16 ], [ 15, 17 ], [ 16 ], [ 19 ], [ 18, 20 ], 
              [ 19 ] ],
          autGroup := Group( [ (18,20), (15,17), (15,18)(16,19)(17,20), (10,11), ( 8, 9), ( 8,10)( 9,11)(12,14), 
              ( 3, 4), ( 1, 2), ( 1, 3)( 2, 4)( 5, 7), ( 1, 8)( 2, 9)( 3,10)( 4,11)( 5,12)( 6,13)( 7,14) ] ),
          forms := [ rec(
                  forms := [ [ "[20, 0, 20]" ], [ "[4, 0, 4]" ] ],
                  h := 220 ), rec(
                  forms := [ [ "[4, 0, 100]" ] ],
                  h := 224 ), rec(
                  forms := [ [ "[8, 4, 52]" ] ],
                  h := 228 ), rec(
                  forms := [ [ "[8, 4, 52]" ] ],
                  h := 232 ), rec(
                  forms := [ [ "[4, 0, 100]" ] ],
                  h := 236 ) ],
          group := Group( [ () ] ),
          h := [ 220, 224, 228, 232, 236 ],
          info := rec(
              bipartite := true,
              distance_regular := false,
              girth := -1,
              pencils := [ [ 3, 4 ], [ 2, 4 ], [ 1, 12 ] ],
              regular := false,
              transitive := -1 ),
          isGraph := true,
          isSimple := true,
          names := [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20 ],
          order := 20,
          real := [  ],
          representatives := [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20 ],
          schreierVector := [ -1, -2, -3, -4, -5, -6, -7, -8, -9, -10, -11, -12, -13, -14, -15, -16, -17, -18, -19, 
              -20 ] ), rec(
          adjacencies := [ [ 7 ], [ 7 ], [ 5 ], [ 5 ], [ 3, 4, 6 ], [ 5, 7 ], [ 1, 2, 6 ], [ 9, 17 ], [ 8, 10 ], 
              [ 9, 11 ], [ 10, 12 ], [ 11, 13 ], [ 12, 14 ], [ 13, 15 ], [ 14, 16 ], [ 15, 17 ], [ 8, 16 ], [ 19 ], 
              [ 18, 20 ], [ 19 ] ],
          autGroup := Group( [ ( 9,17)(10,16)(11,15)(12,14), ( 8, 9)(10,17)(11,16)(12,15)(13,14), ( 3, 4), ( 1, 2), 
              ( 1, 3)( 2, 4)( 5, 7), (18,20) ] ),
          forms := [ rec(
                  forms := [ [ "[4, 0, 40]" ] ],
                  h := 220 ), rec(
                  forms := [ [ "[40, 0, 100]" ] ],
                  h := 224 ), rec(
                  forms := [ [ "[40, 0, 100]" ] ],
                  h := 236 ) ],
          group := Group( [ () ] ),
          h := [ 220, 224, 236 ],
          info := rec(
              bipartite := true,
              distance_regular := false,
              girth := 10,
              pencils := [ [ 3, 2 ], [ 2, 12 ], [ 1, 6 ] ],
              regular := false,
              transitive := -1 ),
          isGraph := true,
          isSimple := true,
          names := [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20 ],
          order := 20,
          real := [  ],
          representatives := [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20 ],
          schreierVector := [ -1, -2, -3, -4, -5, -6, -7, -8, -9, -10, -11, -12, -13, -14, -15, -16, -17, -18, -19, 
              -20 ] ), rec(
          adjacencies := [ [ 7 ], [ 7 ], [ 5 ], [ 5 ], [ 3, 4, 6 ], [ 5, 7 ], [ 1, 2, 6 ], [ 9, 17 ], [ 8, 10 ], 
              [ 9, 11 ], [ 10, 12 ], [ 11, 13 ], [ 12, 14 ], [ 13, 15 ], [ 14, 16 ], [ 15, 17 ], [ 8, 16 ], [ 19 ], 
              [ 18 ], [  ] ],
          autGroup := Group( [ ( 9,17)(10,16)(11,15)(12,14), ( 8, 9)(10,17)(11,16)(12,15)(13,14), (18,19), ( 3, 4), 
              ( 1, 2), ( 1, 3)( 2, 4)( 5, 7) ] ),
          forms := [ rec(
                  forms := [ [ "[16, 4, 16]" ], [ "[4, 2, 16]" ] ],
                  h := 220 ), rec(
                  forms := [ [ "[40, 10, 40]" ], [ "[40, 20, 160]" ] ],
                  h := 224 ), rec(
                  forms := [ [ "[40, 10, 40]" ], [ "[40, 20, 160]" ] ],
                  h := 236 ) ],
          group := Group( [ () ] ),
          h := [ 220, 224, 236 ],
          info := rec(
              bipartite := true,
              distance_regular := false,
              girth := 10,
              pencils := [ [ 3, 2 ], [ 2, 11 ], [ 1, 6 ], [ 0, 1 ] ],
              regular := false,
              transitive := -1 ),
          isGraph := true,
          isSimple := true,
          names := [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20 ],
          order := 20,
          real := [  ],
          representatives := [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20 ],
          schreierVector := [ -1, -2, -3, -4, -5, -6, -7, -8, -9, -10, -11, -12, -13, -14, -15, -16, -17, -18, -19, 
              -20 ] ) ],
  h := [ 220, 222, 224, 226, 228, 230, 232, 234, 236, 238 ],
  hh := [ rec(
          count := [ 20, 21 ],
          deg := 10,
          h := 220,
          real := [  ] ), rec(
          count := [  ],
          deg := 10,
          h := 222,
          real := [  ] ), rec(
          count := [ 20, 21 ],
          deg := 10,
          h := 224,
          real := [  ] ), rec(
          count := [  ],
          deg := 10,
          h := 226,
          real := [  ] ), rec(
          count := [ 20, 21 ],
          deg := 10,
          h := 228,
          real := [  ] ), rec(
          count := [  ],
          deg := 10,
          h := 230,
          real := [  ] ), rec(
          count := [ 20, 21 ],
          deg := 10,
          h := 232,
          real := [  ] ), rec(
          count := [  ],
          deg := 10,
          h := 234,
          real := [  ] ), rec(
          count := [ 20, 21 ],
          deg := 10,
          h := 236,
          real := [  ] ), rec(
          count := [  ],
          deg := 10,
          h := 238,
          real := [  ] ) ] );

