# -*- GAP -*-

a5p_pencil :=
rec(
  graph := [ rec(
          adjacencies := [ [ 2, 6 ], [ 1, 3 ], [ 2, 4 ], [ 3, 5 ], [ 4, 6 ], [ 1, 5 ], [ 8, 12 ], [ 7, 9 ], 
              [ 8, 10 ], [ 9, 11 ], [ 10, 12 ], [ 7, 11 ], [ 14, 18 ], [ 13, 15 ], [ 14, 16 ], [ 15, 17 ], 
              [ 16, 18 ], [ 13, 17 ], [ 20 ], [ 19, 21 ], [ 20 ] ],
          autGroup := Group( [ (14,18)(15,17), (13,14)(15,18)(16,17), ( 8,12)( 9,11), ( 7, 8)( 9,12)(10,11), 
              ( 7,13)( 8,14)( 9,15)(10,16)(11,17)(12,18), ( 2, 6)( 3, 5), ( 1, 2)( 3, 6)( 4, 5), 
              ( 1, 7)( 2, 8)( 3, 9)( 4,10)( 5,11)( 6,12), (19,21) ] ),
          forms := [ rec(
                  forms := [ [ "[4, 0, 24]" ] ],
                  h := 88 ), rec(
                  forms := [ [ "[24, 0, 36]" ] ],
                  h := 92 ) ],
          group := Group( [ () ] ),
          h := [ 88, 92 ],
          info := rec(
              bipartite := true,
              distance_regular := false,
              girth := 6,
              pencils := [ [ 2, 19 ], [ 1, 2 ] ],
              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 := [ [ 2, 6 ], [ 1, 3 ], [ 2, 4 ], [ 3, 5 ], [ 4, 6 ], [ 1, 5 ], [ 8, 12 ], [ 7, 9 ], 
              [ 8, 10 ], [ 9, 11 ], [ 10, 12 ], [ 7, 11 ], [ 14, 18 ], [ 13, 15 ], [ 14, 16 ], [ 15, 17 ], 
              [ 16, 18 ], [ 13, 17 ], [  ], [  ], [  ] ],
          autGroup := Group( [ (14,18)(15,17), (13,14)(15,18)(16,17), ( 8,12)( 9,11), ( 7, 8)( 9,12)(10,11), 
              ( 7,13)( 8,14)( 9,15)(10,16)(11,17)(12,18), ( 2, 6)( 3, 5), ( 1, 2)( 3, 6)( 4, 5), 
              ( 1, 7)( 2, 8)( 3, 9)( 4,10)( 5,11)( 6,12), (20,21), (19,20) ] ),
          forms := [ rec(
                  forms := [ [ "[8, 4, 8]" ] ],
                  h := 84 ), rec(
                  forms := [ [ "[24, 12, 24]" ] ],
                  h := 92 ) ],
          group := Group( [ () ] ),
          h := [ 84, 92 ],
          info := rec(
              bipartite := true,
              distance_regular := false,
              girth := 6,
              pencils := [ [ 2, 18 ], [ 0, 3 ] ],
              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 := [ [ 2, 6 ], [ 1, 3 ], [ 2, 4 ], [ 3, 5 ], [ 4, 6 ], [ 1, 5 ], [ 8, 12 ], [ 7, 9 ], 
              [ 8, 10 ], [ 9, 11 ], [ 10, 12 ], [ 7, 11 ], [ 14, 18 ], [ 13, 15 ], [ 14, 16 ], [ 15, 17 ], 
              [ 16, 18 ], [ 13, 17 ], [ 20 ], [ 19 ] ],
          autGroup := Group( [ (14,18)(15,17), (13,14)(15,18)(16,17), ( 8,12)( 9,11), ( 7, 8)( 9,12)(10,11), 
              ( 7,13)( 8,14)( 9,15)(10,16)(11,17)(12,18), ( 2, 6)( 3, 5), ( 1, 2)( 3, 6)( 4, 5), 
              ( 1, 7)( 2, 8)( 3, 9)( 4,10)( 5,11)( 6,12), (19,20) ] ),
          forms := [ rec(
                  forms := [ [ "[-24] + [4, 2, 4]" ] ],
                  h := 88 ), rec(
                  forms := [ [ "[-24] + [12, 6, 12]" ] ],
                  h := 92 ) ],
          group := Group( [ () ] ),
          h := [ 88, 92 ],
          info := rec(
              bipartite := true,
              distance_regular := false,
              girth := 6,
              pencils := [ [ 2, 18 ], [ 1, 2 ] ],
              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 := [ [ 2, 6 ], [ 1, 3 ], [ 2, 4 ], [ 3, 5 ], [ 4, 6 ], [ 1, 5 ], [ 8, 12 ], [ 7, 9 ], 
              [ 8, 10 ], [ 9, 11 ], [ 10, 12 ], [ 7, 11 ], [ 14, 18 ], [ 13, 15 ], [ 14, 16 ], [ 15, 17 ], 
              [ 16, 18 ], [ 13, 17 ], [  ], [  ] ],
          autGroup := Group( [ (14,18)(15,17), (13,14)(15,18)(16,17), ( 8,12)( 9,11), ( 7, 8)( 9,12)(10,11), 
              ( 7,13)( 8,14)( 9,15)(10,16)(11,17)(12,18), ( 2, 6)( 3, 5), ( 1, 2)( 3, 6)( 4, 5), 
              ( 1, 7)( 2, 8)( 3, 9)( 4,10)( 5,11)( 6,12), (19,20) ] ),
          forms := [ rec(
                  forms := [ [  ] ],
                  h := 84 ), rec(
                  forms := [ [  ] ],
                  h := 88 ), rec(
                  forms := [ [ "U(2) + [24]" ], [ "U(6) + [24]" ] ],
                  h := 92 ) ],
          group := Group( [ () ] ),
          h := [ 84, 88, 92 ],
          info := rec(
              bipartite := true,
              distance_regular := false,
              girth := 6,
              pencils := [ [ 2, 18 ], [ 0, 2 ] ],
              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 := [ 92 ],
          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 := [ [ 2, 6 ], [ 1, 3 ], [ 2, 4 ], [ 3, 5 ], [ 4, 6 ], [ 1, 5 ], [ 8, 12 ], [ 7, 9 ], 
              [ 8, 10 ], [ 9, 11 ], [ 10, 12 ], [ 7, 11 ], [ 14 ], [ 13, 15 ], [ 14, 16 ], [ 15 ], [ 18 ], 
              [ 17, 19 ], [ 18, 20 ], [ 19 ] ],
          autGroup := Group( [ ( 8,12)( 9,11), ( 7, 8)( 9,12)(10,11), ( 2, 6)( 3, 5), ( 1, 2)( 3, 6)( 4, 5), 
              ( 1, 7)( 2, 8)( 3, 9)( 4,10)( 5,11)( 6,12), (17,20)(18,19), (13,16)(14,15), 
              (13,17)(14,18)(15,19)(16,20) ] ),
          forms := [ rec(
                  forms := [ [ "[60, 0, 60]" ] ],
                  h := 92 ) ],
          group := Group( [ () ] ),
          h := [ 92 ],
          info := rec(
              bipartite := true,
              distance_regular := false,
              girth := 6,
              pencils := [ [ 2, 16 ], [ 1, 4 ] ],
              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 := [ [ 2, 6 ], [ 1, 3 ], [ 2, 4 ], [ 3, 5 ], [ 4, 6 ], [ 1, 5 ], [ 8, 12 ], [ 7, 9 ], 
              [ 8, 10 ], [ 9, 11 ], [ 10, 12 ], [ 7, 11 ], [ 14 ], [ 13, 15 ], [ 14, 16 ], [ 15 ], [ 18 ], 
              [ 17, 19 ], [ 18 ], [  ] ],
          autGroup := Group( [ ( 8,12)( 9,11), ( 7, 8)( 9,12)(10,11), ( 2, 6)( 3, 5), ( 1, 2)( 3, 6)( 4, 5), 
              ( 1, 7)( 2, 8)( 3, 9)( 4,10)( 5,11)( 6,12), (13,16)(14,15), (17,19) ] ),
          forms := [ rec(
                  forms := [ [ "[12, 0, 120]" ] ],
                  h := 92 ) ],
          group := Group( [ () ] ),
          h := [ 92 ],
          info := rec(
              bipartite := true,
              distance_regular := false,
              girth := 6,
              pencils := [ [ 2, 15 ], [ 1, 4 ], [ 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 ] ), rec(
          adjacencies := [ [ 2, 6 ], [ 1, 3 ], [ 2, 4 ], [ 3, 5 ], [ 4, 6 ], [ 1, 5 ], [ 8, 12 ], [ 7, 9 ], 
              [ 8, 10 ], [ 9, 11 ], [ 10, 12 ], [ 7, 11 ], [ 14 ], [ 13, 15 ], [ 14, 16 ], [ 15 ], [ 18 ], [ 17 ], 
              [ 20 ], [ 19 ] ],
          autGroup := Group( [ ( 8,12)( 9,11), ( 7, 8)( 9,12)(10,11), ( 2, 6)( 3, 5), ( 1, 2)( 3, 6)( 4, 5), 
              ( 1, 7)( 2, 8)( 3, 9)( 4,10)( 5,11)( 6,12), (19,20), (17,18), (17,19)(18,20), (13,16)(14,15) ] ),
          forms := [ rec(
                  forms := [ [ "[24, 12, 36]" ] ],
                  h := 92 ) ],
          group := Group( [ () ] ),
          h := [ 92 ],
          info := rec(
              bipartite := true,
              distance_regular := false,
              girth := 6,
              pencils := [ [ 2, 14 ], [ 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 := [ [ 2, 6 ], [ 1, 3 ], [ 2, 4 ], [ 3, 5 ], [ 4, 6 ], [ 1, 5 ], [ 8, 12 ], [ 7, 9 ], 
              [ 8, 10 ], [ 9, 11 ], [ 10, 12 ], [ 7, 11 ], [ 14 ], [ 13, 15 ], [ 14 ], [ 17 ], [ 16, 18 ], [ 17 ], 
              [  ], [  ] ],
          autGroup := Group( [ ( 8,12)( 9,11), ( 7, 8)( 9,12)(10,11), ( 2, 6)( 3, 5), ( 1, 2)( 3, 6)( 4, 5), 
              ( 1, 7)( 2, 8)( 3, 9)( 4,10)( 5,11)( 6,12), (16,18), (13,15), (13,16)(14,17)(15,18), (19,20) ] ),
          forms := [ rec(
                  forms := [ [ "[12, 0, 12]" ] ],
                  h := 92 ) ],
          group := Group( [ () ] ),
          h := [ 92 ],
          info := rec(
              bipartite := true,
              distance_regular := false,
              girth := 6,
              pencils := [ [ 2, 14 ], [ 1, 4 ], [ 0, 2 ] ],
              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 := [ [ 2, 6 ], [ 1, 3 ], [ 2, 4 ], [ 3, 5 ], [ 4, 6 ], [ 1, 5 ], [ 8, 12 ], [ 7, 9 ], 
              [ 8, 10 ], [ 9, 11 ], [ 10, 12 ], [ 7, 11 ], [ 14 ], [ 13, 15 ], [ 14 ], [ 17 ], [ 16 ], [ 19 ], 
              [ 18 ], [  ] ],
          autGroup := Group( [ ( 8,12)( 9,11), ( 7, 8)( 9,12)(10,11), ( 2, 6)( 3, 5), ( 1, 2)( 3, 6)( 4, 5), 
              ( 1, 7)( 2, 8)( 3, 9)( 4,10)( 5,11)( 6,12), (18,19), (16,17), (16,18)(17,19), (13,15) ] ),
          forms := [ rec(
                  forms := [ [ "[12, 0, 24]" ] ],
                  h := 92 ) ],
          group := Group( [ () ] ),
          h := [ 92 ],
          info := rec(
              bipartite := true,
              distance_regular := false,
              girth := 6,
              pencils := [ [ 2, 13 ], [ 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 ] ), rec(
          adjacencies := [ [ 2, 6 ], [ 1, 3 ], [ 2, 4 ], [ 3, 5 ], [ 4, 6 ], [ 1, 5 ], [ 8, 12 ], [ 7, 9 ], 
              [ 8, 10 ], [ 9, 11 ], [ 10, 12 ], [ 7, 11 ], [ 14 ], [ 13 ], [ 16 ], [ 15 ], [ 18 ], [ 17 ], [ 20 ], 
              [ 19 ] ],
          autGroup := Group( [ ( 8,12)( 9,11), ( 7, 8)( 9,12)(10,11), ( 2, 6)( 3, 5), ( 1, 2)( 3, 6)( 4, 5), 
              ( 1, 7)( 2, 8)( 3, 9)( 4,10)( 5,11)( 6,12), (19,20), (17,18), (17,19)(18,20), (15,16), (15,17)(16,18), 
              (13,14), (13,15)(14,16) ] ),
          forms := [ rec(
                  forms := [ [ "[12, 0, 12]" ] ],
                  h := 92 ) ],
          group := Group( [ () ] ),
          h := [ 92 ],
          info := rec(
              bipartite := true,
              distance_regular := false,
              girth := 6,
              pencils := [ [ 2, 12 ], [ 1, 8 ] ],
              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 := [ 84, 86, 88, 90, 92, 94 ],
  hh := [ rec(
          count := [ 20, 21 ],
          deg := 6,
          h := 84,
          real := [  ] ), rec(
          count := [  ],
          deg := 6,
          h := 86,
          real := [  ] ), rec(
          count := [ 20, 21 ],
          deg := 6,
          h := 88,
          real := [  ] ), rec(
          count := [  ],
          deg := 6,
          h := 90,
          real := [  ] ), rec(
          count := [ 20, 21 ],
          deg := 6,
          h := 92,
          real := [ 20 ] ), rec(
          count := [  ],
          deg := 6,
          h := 94,
          real := [  ] ) ] );

