function [ a, b, c, w ] = rule24 ( )

%*****************************************************************************80
%
%% rule24() returns the rule of precision 24.
%
%  Licensing:
%
%    This code is distributed under the MIT license.
%
%  Modified:
%
%    09 June 2023
%
%  Author:
%
%    John Burkardt
%
%  Reference:
%
%    Hong Xiao, Zydrunas Gimbutas,
%    A numerical algorithm for the construction of efficient
%    quadrature rules in two and higher dimensions, 
%    Computers and Mathematics with Applications,
%    Volume 59, 2010, pages 663-676.
%
%  Output:
%
%    real a(n), b(n), c(n): the barycentric coordinates of quadrature points.
%
%    real w(n): the quadrature weights.
%
  a = [ ...
          0.3333333333333333, ...
          0.4188909749106027, ...
          0.4188909749106027, ...
          0.1622180501787944, ...
          0.1623606337169263, ...
          0.6752787325661472, ...
          0.1623606337169265, ...
          0.2414797600735940, ...
          0.5881529574639622, ...
          0.1703672824624437, ...
          0.5881529574639622, ...
          0.2414797600735940, ...
          0.1703672824624436, ...
          0.3289758089242263, ...
          0.5012643952150375, ...
          0.1697597958607360, ...
          0.5012643952150376, ...
          0.3289758089242264, ...
          0.1697597958607359, ...
          0.0409856290011169, ...
          0.9180287419977657, ...
          0.0409856290011174, ...
          0.0067312708878883, ...
          0.9865374582242232, ...
          0.0067312708878887, ...
          0.0931674097798811, ...
          0.8685143643990995, ...
          0.0383182258210195, ...
          0.8685143643990995, ...
          0.0931674097798812, ...
          0.0383182258210191, ...
          0.3945202798001943, ...
          0.5128232386790481, ...
          0.0926564815207574, ...
          0.5128232386790481, ...
          0.3945202798001944, ...
          0.0926564815207574, ...
          0.1626774163944774, ...
          0.7961338693570472, ...
          0.0411887142484756, ...
          0.7961338693570472, ...
          0.1626774163944775, ...
          0.0411887142484752, ...
          0.2535890142188795, ...
          0.7068400808109625, ...
          0.0395709049701581, ...
          0.7068400808109625, ...
          0.2535890142188795, ...
          0.0395709049701579, ...
          0.3622522413177913, ...
          0.5991550585073127, ...
          0.0385927001748961, ...
          0.5991550585073125, ...
          0.3622522413177913, ...
          0.0385927001748960, ...
          0.2816225777061608, ...
          0.6238424605572400, ...
          0.0945349617365990, ...
          0.6238424605572401, ...
          0.2816225777061608, ...
          0.0945349617365988, ...
          0.3832726649926592, ...
          0.6093393403750466, ...
          0.0073879946322942, ...
          0.6093393403750464, ...
          0.3832726649926592, ...
          0.0073879946322941, ...
          0.2737503525162605, ...
          0.7187036443214266, ...
          0.0075460031623129, ...
          0.7187036443214266, ...
          0.2737503525162606, ...
          0.0075460031623126, ...
          0.4962552776757351, ...
          0.4962552776757351, ...
          0.0074894446485297, ...
          0.0941213427973660, ...
          0.8986440987448518, ...
          0.0072345584577822, ...
          0.8986440987448518, ...
          0.0941213427973661, ...
          0.0072345584577819, ...
          0.2642313154382725, ...
          0.4715373691234548, ...
          0.2642313154382727, ...
          0.1803961518867657, ...
          0.7240375785858689, ...
          0.0955662695273654, ...
          0.7240375785858689, ...
          0.1803961518867657, ...
          0.0955662695273650, ...
          0.4806125617925032, ...
          0.4806125617925033, ...
          0.0387748764149934, ...
          0.1747373462828057, ...
          0.8172747318363464, ...
          0.0079879218808480, ...
          0.8172747318363462, ...
          0.1747373462828057, ...
          0.0079879218808478, ...
          0.0963284955992151, ...
          0.8073430088015696, ...
          0.0963284955992154, ...
          0.0372914720512912, ...
          0.9546336170785000, ...
          0.0080749108702090, ...
          0.9546336170785000, ...
          0.0372914720512914, ...
          0.0080749108702085, ...
          0.3753529267020863, ...
          0.3753529267020863, ...
          0.2492941465958274 ];

  b = [ ...
          0.3333333333333334, ...
          0.1622180501787945, ...
          0.4188909749106028, ...
          0.4188909749106029, ...
          0.1623606337169265, ...
          0.1623606337169263, ...
          0.6752787325661475, ...
          0.1703672824624437, ...
          0.2414797600735941, ...
          0.5881529574639625, ...
          0.1703672824624437, ...
          0.5881529574639625, ...
          0.2414797600735942, ...
          0.1697597958607361, ...
          0.3289758089242264, ...
          0.5012643952150377, ...
          0.1697597958607361, ...
          0.5012643952150377, ...
          0.3289758089242266, ...
          0.0409856290011173, ...
          0.0409856290011169, ...
          0.9180287419977659, ...
          0.0067312708878885, ...
          0.0067312708878882, ...
          0.9865374582242232, ...
          0.0383182258210194, ...
          0.0931674097798812, ...
          0.8685143643990996, ...
          0.0383182258210194, ...
          0.8685143643990996, ...
          0.0931674097798815, ...
          0.0926564815207575, ...
          0.3945202798001944, ...
          0.5128232386790483, ...
          0.0926564815207575, ...
          0.5128232386790482, ...
          0.3945202798001946, ...
          0.0411887142484754, ...
          0.1626774163944774, ...
          0.7961338693570472, ...
          0.0411887142484754, ...
          0.7961338693570472, ...
          0.1626774163944777, ...
          0.0395709049701581, ...
          0.2535890142188795, ...
          0.7068400808109626, ...
          0.0395709049701581, ...
          0.7068400808109626, ...
          0.2535890142188797, ...
          0.0385927001748961, ...
          0.3622522413177914, ...
          0.5991550585073128, ...
          0.0385927001748961, ...
          0.5991550585073127, ...
          0.3622522413177915, ...
          0.0945349617365990, ...
          0.2816225777061609, ...
          0.6238424605572404, ...
          0.0945349617365990, ...
          0.6238424605572404, ...
          0.2816225777061611, ...
          0.0073879946322942, ...
          0.3832726649926593, ...
          0.6093393403750468, ...
          0.0073879946322942, ...
          0.6093393403750467, ...
          0.3832726649926595, ...
          0.0075460031623128, ...
          0.2737503525162605, ...
          0.7187036443214270, ...
          0.0075460031623128, ...
          0.7187036443214267, ...
          0.2737503525162608, ...
          0.0074894446485298, ...
          0.4962552776757352, ...
          0.4962552776757354, ...
          0.0072345584577821, ...
          0.0941213427973660, ...
          0.8986440987448521, ...
          0.0072345584577821, ...
          0.8986440987448520, ...
          0.0941213427973664, ...
          0.2642313154382727, ...
          0.2642313154382726, ...
          0.4715373691234549, ...
          0.0955662695273653, ...
          0.1803961518867657, ...
          0.7240375785858691, ...
          0.0955662695273653, ...
          0.7240375785858693, ...
          0.1803961518867660, ...
          0.0387748764149935, ...
          0.4806125617925033, ...
          0.4806125617925034, ...
          0.0079879218808480, ...
          0.1747373462828057, ...
          0.8172747318363466, ...
          0.0079879218808480, ...
          0.8172747318363466, ...
          0.1747373462828060, ...
          0.0963284955992153, ...
          0.0963284955992151, ...
          0.8073430088015697, ...
          0.0080749108702088, ...
          0.0372914720512912, ...
          0.9546336170785000, ...
          0.0080749108702088, ...
          0.9546336170785000, ...
          0.0372914720512916, ...
          0.2492941465958275, ...
          0.3753529267020864, ...
          0.3753529267020864 ];

  c = [ ...
          0.3333333333333333, ...
          0.4188909749106028, ...
          0.1622180501787945, ...
          0.4188909749106027, ...
          0.6752787325661472, ...
          0.1623606337169265, ...
          0.1623606337169260, ...
          0.5881529574639622, ...
          0.1703672824624437, ...
          0.2414797600735938, ...
          0.2414797600735940, ...
          0.1703672824624435, ...
          0.5881529574639621, ...
          0.5012643952150376, ...
          0.1697597958607361, ...
          0.3289758089242263, ...
          0.3289758089242263, ...
          0.1697597958607359, ...
          0.5012643952150375, ...
          0.9180287419977659, ...
          0.0409856290011173, ...
          0.0409856290011167, ...
          0.9865374582242232, ...
          0.0067312708878886, ...
          0.0067312708878881, ...
          0.8685143643990995, ...
          0.0383182258210194, ...
          0.0931674097798809, ...
          0.0931674097798811, ...
          0.0383182258210192, ...
          0.8685143643990995, ...
          0.5128232386790481, ...
          0.0926564815207574, ...
          0.3945202798001942, ...
          0.3945202798001943, ...
          0.0926564815207574, ...
          0.5128232386790480, ...
          0.7961338693570472, ...
          0.0411887142484754, ...
          0.1626774163944772, ...
          0.1626774163944774, ...
          0.0411887142484753, ...
          0.7961338693570471, ...
          0.7068400808109625, ...
          0.0395709049701580, ...
          0.2535890142188794, ...
          0.2535890142188795, ...
          0.0395709049701579, ...
          0.7068400808109623, ...
          0.5991550585073125, ...
          0.0385927001748960, ...
          0.3622522413177912, ...
          0.3622522413177913, ...
          0.0385927001748960, ...
          0.5991550585073124, ...
          0.6238424605572401, ...
          0.0945349617365990, ...
          0.2816225777061607, ...
          0.2816225777061608, ...
          0.0945349617365988, ...
          0.6238424605572401, ...
          0.6093393403750466, ...
          0.0073879946322942, ...
          0.3832726649926591, ...
          0.3832726649926593, ...
          0.0073879946322941, ...
          0.6093393403750464, ...
          0.7187036443214266, ...
          0.0075460031623129, ...
          0.2737503525162601, ...
          0.2737503525162606, ...
          0.0075460031623127, ...
          0.7187036443214266, ...
          0.4962552776757350, ...
          0.0074894446485297, ...
          0.4962552776757349, ...
          0.8986440987448518, ...
          0.0072345584577821, ...
          0.0941213427973657, ...
          0.0941213427973660, ...
          0.0072345584577819, ...
          0.8986440987448517, ...
          0.4715373691234548, ...
          0.2642313154382726, ...
          0.2642313154382724, ...
          0.7240375785858690, ...
          0.0955662695273653, ...
          0.1803961518867655, ...
          0.1803961518867658, ...
          0.0955662695273650, ...
          0.7240375785858690, ...
          0.4806125617925033, ...
          0.0387748764149934, ...
          0.4806125617925031, ...
          0.8172747318363464, ...
          0.0079879218808480, ...
          0.1747373462828054, ...
          0.1747373462828058, ...
          0.0079879218808477, ...
          0.8172747318363462, ...
          0.8073430088015696, ...
          0.0963284955992153, ...
          0.0963284955992149, ...
          0.9546336170785000, ...
          0.0080749108702088, ...
          0.0372914720512910, ...
          0.0372914720512912, ...
          0.0080749108702086, ...
          0.9546336170784999, ...
          0.3753529267020862, ...
          0.2492941465958273, ...
          0.3753529267020862 ];

  w = [ ...
          0.0125456898456003, ...
          0.0131105327018852, ...
          0.0131105327018852, ...
          0.0131105327018852, ...
          0.0103790160564002, ...
          0.0103790160564002, ...
          0.0103790160564002, ...
          0.0141450458064848, ...
          0.0141450458064848, ...
          0.0141450458064848, ...
          0.0141450458064848, ...
          0.0141450458064848, ...
          0.0141450458064848, ...
          0.0152744426013246, ...
          0.0152744426013246, ...
          0.0152744426013246, ...
          0.0152744426013246, ...
          0.0152744426013246, ...
          0.0152744426013246, ...
          0.0038336997309292, ...
          0.0038336997309292, ...
          0.0038336997309292, ...
          0.0006172545054966, ...
          0.0006172545054966, ...
          0.0006172545054966, ...
          0.0053662714541678, ...
          0.0053662714541678, ...
          0.0053662714541678, ...
          0.0053662714541678, ...
          0.0053662714541678, ...
          0.0053662714541678, ...
          0.0150318543497413, ...
          0.0150318543497413, ...
          0.0150318543497413, ...
          0.0150318543497413, ...
          0.0150318543497413, ...
          0.0150318543497413, ...
          0.0072041341747974, ...
          0.0072041341747974, ...
          0.0072041341747974, ...
          0.0072041341747974, ...
          0.0072041341747974, ...
          0.0072041341747974, ...
          0.0089048769281636, ...
          0.0089048769281636, ...
          0.0089048769281636, ...
          0.0089048769281636, ...
          0.0089048769281636, ...
          0.0089048769281636, ...
          0.0099472518756824, ...
          0.0099472518756824, ...
          0.0099472518756824, ...
          0.0099472518756824, ...
          0.0099472518756824, ...
          0.0099472518756824, ...
          0.0143523515781575, ...
          0.0143523515781575, ...
          0.0143523515781575, ...
          0.0143523515781575, ...
          0.0143523515781575, ...
          0.0143523515781575, ...
          0.0042421492668038, ...
          0.0042421492668038, ...
          0.0042421492668038, ...
          0.0042421492668038, ...
          0.0042421492668038, ...
          0.0042421492668038, ...
          0.0040812750771165, ...
          0.0040812750771165, ...
          0.0040812750771165, ...
          0.0040812750771165, ...
          0.0040812750771165, ...
          0.0040812750771165, ...
          0.0043432467221707, ...
          0.0043432467221707, ...
          0.0043432467221707, ...
          0.0025892123823980, ...
          0.0025892123823980, ...
          0.0025892123823980, ...
          0.0025892123823980, ...
          0.0025892123823980, ...
          0.0025892123823980, ...
          0.0205200086715098, ...
          0.0205200086715098, ...
          0.0205200086715098, ...
          0.0118435621425431, ...
          0.0118435621425431, ...
          0.0118435621425431, ...
          0.0118435621425431, ...
          0.0118435621425431, ...
          0.0118435621425431, ...
          0.0103524947708526, ...
          0.0103524947708526, ...
          0.0103524947708526, ...
          0.0037072267642463, ...
          0.0037072267642463, ...
          0.0037072267642463, ...
          0.0037072267642463, ...
          0.0037072267642463, ...
          0.0037072267642463, ...
          0.0100273930673889, ...
          0.0100273930673889, ...
          0.0100273930673889, ...
          0.0017969475854466, ...
          0.0017969475854466, ...
          0.0017969475854466, ...
          0.0017969475854466, ...
          0.0017969475854466, ...
          0.0017969475854466, ...
          0.0189945865173527, ...
          0.0189945865173527, ...
          0.0189945865173527 ];

  return
end
