# -*- GAP -*-

a4p_pencil :=
rec(
  graph := [ rec(
          adjacencies := [ [ 2, 5 ], [ 1, 3 ], [ 2, 4 ], [ 3, 5 ], [ 1, 4 ], [ 7, 10 ], [ 6, 8 ], [ 7, 9 ], 
              [ 8, 10 ], [ 6, 9 ], [ 12, 15 ], [ 11, 13 ], [ 12, 14 ], [ 13, 15 ], [ 11, 14 ], [ 17, 20 ], 
              [ 16, 18 ], [ 17, 19 ], [ 18, 20 ], [ 16, 19 ], [  ], [  ] ],
          autGroup := Group( [ (17,20)(18,19), (16,17)(18,20), (12,15)(13,14), (11,12)(13,15), 
              (11,16)(12,17)(13,18)(14,19)(15,20), ( 7,10)( 8, 9), ( 6, 7)( 8,10), ( 6,11)( 7,12)( 8,13)( 9,14)(10,15)
                , ( 2, 5)( 3, 4), ( 1, 2)( 3, 5), ( 1, 6)( 2, 7)( 3, 8)( 4, 9)( 5,10), (21,22) ] ),
          forms := [ rec(
                  forms := [ [ "[10, 0, 10]" ] ],
                  h := 64 ) ],
          group := Group( [ () ] ),
          h := [ 64 ],
          info := rec(
              bipartite := false,
              distance_regular := false,
              girth := 5,
              pencils := [ [ 2, 20 ], [ 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, 21, 22 ],
          order := 22,
          real := [  ],
          representatives := [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22 ],
          schreierVector := [ -1, -2, -3, -4, -5, -6, -7, -8, -9, -10, -11, -12, -13, -14, -15, -16, -17, -18, -19, 
              -20, -21, -22 ] ), rec(
          adjacencies := [ [ 2, 5 ], [ 1, 3 ], [ 2, 4 ], [ 3, 5 ], [ 1, 4 ], [ 7, 10 ], [ 6, 8 ], [ 7, 9 ], 
              [ 8, 10 ], [ 6, 9 ], [ 12, 15 ], [ 11, 13 ], [ 12, 14 ], [ 13, 15 ], [ 11, 14 ], [ 17, 20 ], 
              [ 16, 18 ], [ 17, 19 ], [ 18, 20 ], [ 16, 19 ], [  ] ],
          autGroup := Group( [ (17,20)(18,19), (16,17)(18,20), (12,15)(13,14), (11,12)(13,15), 
              (11,16)(12,17)(13,18)(14,19)(15,20), ( 7,10)( 8, 9), ( 6, 7)( 8,10), ( 6,11)( 7,12)( 8,13)( 9,14)(10,15)
                , ( 2, 5)( 3, 4), ( 1, 2)( 3, 5), ( 1, 6)( 2, 7)( 3, 8)( 4, 9)( 5,10) ] ),
          forms := [ rec(
                  forms := [ [ "U(5) + [50]" ] ],
                  h := 60 ), rec(
                  forms := [ [ "U(5) + [2]" ] ],
                  h := 62 ), rec(
                  forms := [ [ "U(5) + [50]" ] ],
                  h := 64 ) ],
          group := Group( [ () ] ),
          h := [ 60, 62, 64 ],
          info := rec(
              bipartite := false,
              distance_regular := false,
              girth := 5,
              pencils := [ [ 2, 20 ], [ 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, 21 ],
          order := 21,
          real := [ 62 ],
          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, 5 ], [ 1, 3 ], [ 2, 4 ], [ 3, 5 ], [ 1, 4 ], [ 7, 10 ], [ 6, 8 ], [ 7, 9 ], 
              [ 8, 10 ], [ 6, 9 ], [ 12, 15 ], [ 11, 13 ], [ 12, 14 ], [ 13, 15 ], [ 11, 14 ], [ 17, 20 ], 
              [ 16, 18 ], [ 17, 19 ], [ 18, 20 ], [ 16, 19 ] ],
          autGroup := Group( [ (17,20)(18,19), (16,17)(18,20), (12,15)(13,14), (11,12)(13,15), 
              (11,16)(12,17)(13,18)(14,19)(15,20), ( 7,10)( 8, 9), ( 6, 7)( 8,10), ( 6,11)( 7,12)( 8,13)( 9,14)(10,15)
                , ( 2, 5)( 3, 4), ( 1, 2)( 3, 5), ( 1, 6)( 2, 7)( 3, 8)( 4, 9)( 5,10) ] ),
          forms := [ rec(
                  forms := [ [ "U(1) + U(5)" ], [ "U(5) + U(5)" ] ],
                  h := 60 ), rec(
                  forms := [ [  ] ],
                  h := 62 ), rec(
                  forms := [ [  ] ],
                  h := 64 ), rec(
                  forms := [ [  ] ],
                  h := 66 ), rec(
                  forms := [ [  ] ],
                  h := 68 ) ],
          group := Group( [ () ] ),
          h := [ 60, 62, 64, 66, 68 ],
          info := rec(
              bipartite := false,
              distance_regular := false,
              girth := 5,
              pencils := [ [ 2, 20 ] ],
              regular := 2,
              transitive := 4 ),
          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 := [ 60, 62, 68 ],
          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, 5 ], [ 1, 3 ], [ 2, 4 ], [ 3, 5 ], [ 1, 4 ], [ 7, 10 ], [ 6, 8 ], [ 7, 9 ], 
              [ 8, 10 ], [ 6, 9 ], [ 12, 15 ], [ 11, 13 ], [ 12, 14 ], [ 13, 15 ], [ 11, 14 ], [ 17 ], [ 16, 18 ], 
              [ 17 ], [  ], [  ] ],
          autGroup := Group( [ (12,15)(13,14), (11,12)(13,15), ( 7,10)( 8, 9), ( 6, 7)( 8,10), 
              ( 6,11)( 7,12)( 8,13)( 9,14)(10,15), ( 2, 5)( 3, 4), ( 1, 2)( 3, 5), ( 1, 6)( 2, 7)( 3, 8)( 4, 9)( 5,10)
                , (16,18), (19,20) ] ),
          forms := [ rec(
                  forms := [ [ "[-20] + [10] + [10]", "[-10] + [10] + [20]" ] ],
                  h := 64 ) ],
          group := Group( [ () ] ),
          h := [ 64 ],
          info := rec(
              bipartite := false,
              distance_regular := false,
              girth := 5,
              pencils := [ [ 2, 16 ], [ 1, 2 ], [ 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, 5 ], [ 1, 3 ], [ 2, 4 ], [ 3, 5 ], [ 1, 4 ], [ 7, 10 ], [ 6, 8 ], [ 7, 9 ], 
              [ 8, 10 ], [ 6, 9 ], [ 12, 15 ], [ 11, 13 ], [ 12, 14 ], [ 13, 15 ], [ 11, 14 ], [ 17 ], [ 16 ], [  ], 
              [  ], [  ] ],
          autGroup := Group( [ (12,15)(13,14), (11,12)(13,15), ( 7,10)( 8, 9), ( 6, 7)( 8,10), 
              ( 6,11)( 7,12)( 8,13)( 9,14)(10,15), ( 2, 5)( 3, 4), ( 1, 2)( 3, 5), ( 1, 6)( 2, 7)( 3, 8)( 4, 9)( 5,10)
                , (16,17), (19,20), (18,19) ] ),
          forms := [ rec(
                  forms := [ [ "[-30] + [10] + [10]", "[-10] + [20, 10, 20]" ] ],
                  h := 64 ) ],
          group := Group( [ () ] ),
          h := [ 64 ],
          info := rec(
              bipartite := false,
              distance_regular := false,
              girth := 5,
              pencils := [ [ 2, 15 ], [ 1, 2 ], [ 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 ],
          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, 5 ], [ 1, 3 ], [ 2, 4 ], [ 3, 5 ], [ 1, 4 ], [ 7, 10 ], [ 6, 8 ], [ 7, 9 ], 
              [ 8, 10 ], [ 6, 9 ], [ 12 ], [ 11, 13 ], [ 12 ], [ 15 ], [ 14, 16 ], [ 15 ], [ 18 ], [ 17 ], [ 20 ], 
              [ 19 ] ],
          autGroup := Group( [ ( 7,10)( 8, 9), ( 6, 7)( 8,10), ( 2, 5)( 3, 4), ( 1, 2)( 3, 5), 
              ( 1, 6)( 2, 7)( 3, 8)( 4, 9)( 5,10), (19,20), (17,18), (17,19)(18,20), (14,16), (11,13), 
              (11,14)(12,15)(13,16) ] ),
          forms := [ rec(
                  forms := [ [ "[60, 0, 60]" ] ],
                  h := 66 ) ],
          group := Group( [ () ] ),
          h := [ 66 ],
          info := rec(
              bipartite := false,
              distance_regular := false,
              girth := 5,
              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 := [ 60, 62, 64, 66, 68 ],
  hh := [ rec(
          count := [ 20, 21 ],
          deg := 5,
          h := 60,
          real := [ 20 ] ), rec(
          count := [ 20, 21 ],
          deg := 5,
          h := 62,
          real := [ 20, 21 ] ), rec(
          count := [ 20, 21, 22 ],
          deg := 5,
          h := 64,
          real := [  ] ), rec(
          count := [ 20 ],
          deg := 5,
          h := 66,
          real := [  ] ), rec(
          count := [ 20 ],
          deg := 5,
          h := 68,
          real := [ 20 ] ) ] );

