function [ a, b, c, w ] = rule23 ( )

%*****************************************************************************80
%
%% rule23() returns the rule of precision 23.
%
%  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 = [ ...
          0.1595037989247572, ...
          0.8166259474208891, ...
          0.0238702536543537, ...
          0.8166259474208892, ...
          0.1595037989247573, ...
          0.0238702536543534, ...
          0.1141013603223645, ...
          0.8807088179167908, ...
          0.0051898217608446, ...
          0.8807088179167909, ...
          0.1141013603223646, ...
          0.0051898217608443, ...
          0.0390072687570320, ...
          0.9219854624859357, ...
          0.0390072687570324, ...
          0.0955398781717349, ...
          0.8717190926395586, ...
          0.0327410291887065, ...
          0.8717190926395587, ...
          0.0955398781717349, ...
          0.0327410291887062, ...
          0.3111622680517019, ...
          0.6863901320923316, ...
          0.0024475998559664, ...
          0.6863901320923317, ...
          0.3111622680517019, ...
          0.0024475998559662, ...
          0.2056172320580521, ...
          0.7856574783566395, ...
          0.0087252895853085, ...
          0.7856574783566393, ...
          0.2056172320580521, ...
          0.0087252895853083, ...
          0.0472616294497253, ...
          0.9455758306400303, ...
          0.0071625399102447, ...
          0.9455758306400303, ...
          0.0472616294497255, ...
          0.0071625399102442, ...
          0.3585095935696251, ...
          0.5729634522431619, ...
          0.0685269541872131, ...
          0.5729634522431619, ...
          0.3585095935696250, ...
          0.0685269541872129, ...
          0.4803288773373085, ...
          0.4803288773373085, ...
          0.0393422453253830, ...
          0.2404827720350127, ...
          0.6577888986377031, ...
          0.1017283293272843, ...
          0.6577888986377032, ...
          0.2404827720350126, ...
          0.1017283293272841, ...
          0.0868410482076331, ...
          0.8263179035847337, ...
          0.0868410482076334, ...
          0.3943235060115415, ...
          0.3943235060115415, ...
          0.2113529879769169, ...
          0.2662513178772472, ...
          0.4674973642455053, ...
          0.2662513178772474, ...
          0.1729323031292240, ...
          0.7687161216332605, ...
          0.0583515752375156, ...
          0.7687161216332605, ...
          0.1729323031292240, ...
          0.0583515752375153, ...
          0.3163043076538381, ...
          0.5288655369406456, ...
          0.1548301554055163, ...
          0.5288655369406456, ...
          0.3163043076538382, ...
          0.1548301554055161, ...
          0.1371293873116475, ...
          0.7257412253767047, ...
          0.1371293873116478, ...
          0.4989594312095863, ...
          0.4989594312095863, ...
          0.0020811375808273, ...
          0.3977585768030076, ...
          0.5874824534670471, ...
          0.0147589697299451, ...
          0.5874824534670471, ...
          0.3977585768030076, ...
          0.0147589697299450, ...
          0.4446924421277275, ...
          0.4446924421277275, ...
          0.1106151157445449, ...
          0.1987498063965361, ...
          0.6025003872069274, ...
          0.1987498063965363, ...
          0.2787941698141023, ...
          0.6882121219933649, ...
          0.0329937081925328, ...
          0.6882121219933649, ...
          0.2787941698141023, ...
          0.0329937081925327, ...
          0.0090164402055982, ...
          0.9819671195888033, ...
          0.0090164402055986, ...
          0.3333333333333333 ];

  b = [ ...
          0.0238702536543536, ...
          0.1595037989247572, ...
          0.8166259474208892, ...
          0.0238702536543536, ...
          0.8166259474208892, ...
          0.1595037989247576, ...
          0.0051898217608445, ...
          0.1141013603223645, ...
          0.8807088179167911, ...
          0.0051898217608445, ...
          0.8807088179167911, ...
          0.1141013603223648, ...
          0.0390072687570323, ...
          0.0390072687570320, ...
          0.9219854624859359, ...
          0.0327410291887064, ...
          0.0955398781717349, ...
          0.8717190926395588, ...
          0.0327410291887064, ...
          0.8717190926395588, ...
          0.0955398781717352, ...
          0.0024475998559664, ...
          0.3111622680517020, ...
          0.6863901320923319, ...
          0.0024475998559664, ...
          0.6863901320923319, ...
          0.3111622680517022, ...
          0.0087252895853085, ...
          0.2056172320580521, ...
          0.7856574783566396, ...
          0.0087252895853085, ...
          0.7856574783566396, ...
          0.2056172320580524, ...
          0.0071625399102445, ...
          0.0472616294497253, ...
          0.9455758306400303, ...
          0.0071625399102445, ...
          0.9455758306400303, ...
          0.0472616294497257, ...
          0.0685269541872130, ...
          0.3585095935696251, ...
          0.5729634522431620, ...
          0.0685269541872130, ...
          0.5729634522431620, ...
          0.3585095935696253, ...
          0.0393422453253830, ...
          0.4803288773373086, ...
          0.4803288773373087, ...
          0.1017283293272843, ...
          0.2404827720350127, ...
          0.6577888986377033, ...
          0.1017283293272843, ...
          0.6577888986377033, ...
          0.2404827720350129, ...
          0.0868410482076333, ...
          0.0868410482076330, ...
          0.8263179035847338, ...
          0.2113529879769170, ...
          0.3943235060115416, ...
          0.3943235060115416, ...
          0.2662513178772474, ...
          0.2662513178772473, ...
          0.4674973642455055, ...
          0.0583515752375155, ...
          0.1729323031292239, ...
          0.7687161216332608, ...
          0.0583515752375155, ...
          0.7687161216332608, ...
          0.1729323031292242, ...
          0.1548301554055163, ...
          0.3163043076538382, ...
          0.5288655369406458, ...
          0.1548301554055163, ...
          0.5288655369406458, ...
          0.3163043076538383, ...
          0.1371293873116478, ...
          0.1371293873116475, ...
          0.7257412253767048, ...
          0.0020811375808274, ...
          0.4989594312095864, ...
          0.4989594312095865, ...
          0.0147589697299452, ...
          0.3977585768030077, ...
          0.5874824534670474, ...
          0.0147589697299452, ...
          0.5874824534670473, ...
          0.3977585768030079, ...
          0.1106151157445450, ...
          0.4446924421277276, ...
          0.4446924421277277, ...
          0.1987498063965364, ...
          0.1987498063965362, ...
          0.6025003872069277, ...
          0.0329937081925328, ...
          0.2787941698141023, ...
          0.6882121219933651, ...
          0.0329937081925328, ...
          0.6882121219933650, ...
          0.2787941698141025, ...
          0.0090164402055985, ...
          0.0090164402055982, ...
          0.9819671195888034, ...
          0.3333333333333334 ];

  c = [ ...
          0.8166259474208892, ...
          0.0238702536543536, ...
          0.1595037989247570, ...
          0.1595037989247572, ...
          0.0238702536543535, ...
          0.8166259474208891, ...
          0.8807088179167910, ...
          0.0051898217608447, ...
          0.1141013603223643, ...
          0.1141013603223646, ...
          0.0051898217608443, ...
          0.8807088179167908, ...
          0.9219854624859357, ...
          0.0390072687570323, ...
          0.0390072687570316, ...
          0.8717190926395586, ...
          0.0327410291887065, ...
          0.0955398781717347, ...
          0.0955398781717349, ...
          0.0327410291887062, ...
          0.8717190926395585, ...
          0.6863901320923317, ...
          0.0024475998559664, ...
          0.3111622680517018, ...
          0.3111622680517019, ...
          0.0024475998559662, ...
          0.6863901320923316, ...
          0.7856574783566395, ...
          0.0087252895853084, ...
          0.2056172320580519, ...
          0.2056172320580521, ...
          0.0087252895853084, ...
          0.7856574783566393, ...
          0.9455758306400301, ...
          0.0071625399102445, ...
          0.0472616294497251, ...
          0.0472616294497253, ...
          0.0071625399102443, ...
          0.9455758306400301, ...
          0.5729634522431619, ...
          0.0685269541872129, ...
          0.3585095935696249, ...
          0.3585095935696251, ...
          0.0685269541872130, ...
          0.5729634522431618, ...
          0.4803288773373085, ...
          0.0393422453253830, ...
          0.4803288773373083, ...
          0.6577888986377031, ...
          0.1017283293272842, ...
          0.2404827720350124, ...
          0.2404827720350126, ...
          0.1017283293272840, ...
          0.6577888986377031, ...
          0.8263179035847337, ...
          0.0868410482076333, ...
          0.0868410482076328, ...
          0.3943235060115415, ...
          0.2113529879769168, ...
          0.3943235060115414, ...
          0.4674973642455054, ...
          0.2662513178772473, ...
          0.2662513178772471, ...
          0.7687161216332605, ...
          0.0583515752375155, ...
          0.1729323031292237, ...
          0.1729323031292240, ...
          0.0583515752375152, ...
          0.7687161216332604, ...
          0.5288655369406456, ...
          0.1548301554055162, ...
          0.3163043076538380, ...
          0.3163043076538381, ...
          0.1548301554055161, ...
          0.5288655369406455, ...
          0.7257412253767047, ...
          0.1371293873116478, ...
          0.1371293873116474, ...
          0.4989594312095863, ...
          0.0020811375808273, ...
          0.4989594312095861, ...
          0.5874824534670472, ...
          0.0147589697299452, ...
          0.3977585768030075, ...
          0.3977585768030077, ...
          0.0147589697299451, ...
          0.5874824534670471, ...
          0.4446924421277275, ...
          0.1106151157445449, ...
          0.4446924421277273, ...
          0.6025003872069276, ...
          0.1987498063965363, ...
          0.1987498063965361, ...
          0.6882121219933649, ...
          0.0329937081925328, ...
          0.2787941698141020, ...
          0.2787941698141023, ...
          0.0329937081925327, ...
          0.6882121219933648, ...
          0.9819671195888033, ...
          0.0090164402055985, ...
          0.0090164402055980, ...
          0.3333333333333333 ];

  w = [ ...
          0.0025281660553823, ...
          0.0025281660553823, ...
          0.0025281660553823, ...
          0.0025281660553823, ...
          0.0025281660553823, ...
          0.0025281660553823, ...
          0.0022250197297245, ...
          0.0022250197297245, ...
          0.0022250197297245, ...
          0.0022250197297245, ...
          0.0022250197297245, ...
          0.0022250197297245, ...
          0.0039157402590329, ...
          0.0039157402590329, ...
          0.0039157402590329, ...
          0.0053280304311948, ...
          0.0053280304311948, ...
          0.0053280304311948, ...
          0.0053280304311948, ...
          0.0053280304311948, ...
          0.0053280304311948, ...
          0.0022811036762558, ...
          0.0022811036762558, ...
          0.0022811036762558, ...
          0.0022811036762558, ...
          0.0022811036762558, ...
          0.0022811036762558, ...
          0.0041147503444161, ...
          0.0041147503444161, ...
          0.0041147503444161, ...
          0.0041147503444161, ...
          0.0041147503444161, ...
          0.0041147503444161, ...
          0.0019525913278907, ...
          0.0019525913278907, ...
          0.0019525913278907, ...
          0.0019525913278907, ...
          0.0019525913278907, ...
          0.0019525913278907, ...
          0.0149811133931992, ...
          0.0149811133931992, ...
          0.0149811133931992, ...
          0.0149811133931992, ...
          0.0149811133931992, ...
          0.0149811133931992, ...
          0.0113978892678008, ...
          0.0113978892678008, ...
          0.0113978892678008, ...
          0.0161212416370172, ...
          0.0161212416370172, ...
          0.0161212416370172, ...
          0.0161212416370172, ...
          0.0161212416370172, ...
          0.0161212416370172, ...
          0.0089599170255135, ...
          0.0089599170255135, ...
          0.0089599170255135, ...
          0.0236746084631280, ...
          0.0236746084631280, ...
          0.0236746084631280, ...
          0.0238078628874998, ...
          0.0238078628874998, ...
          0.0238078628874998, ...
          0.0104702564931301, ...
          0.0104702564931301, ...
          0.0104702564931301, ...
          0.0104702564931301, ...
          0.0104702564931301, ...
          0.0104702564931301, ...
          0.0208443958589688, ...
          0.0208443958589688, ...
          0.0208443958589688, ...
          0.0208443958589688, ...
          0.0208443958589688, ...
          0.0208443958589688, ...
          0.0145594493927417, ...
          0.0145594493927417, ...
          0.0145594493927417, ...
          0.0024075446041814, ...
          0.0024075446041814, ...
          0.0024075446041814, ...
          0.0070977788345218, ...
          0.0070977788345218, ...
          0.0070977788345218, ...
          0.0070977788345218, ...
          0.0070977788345218, ...
          0.0070977788345218, ...
          0.0189519506693389, ...
          0.0189519506693389, ...
          0.0189519506693389, ...
          0.0199352778801050, ...
          0.0199352778801050, ...
          0.0199352778801050, ...
          0.0101755746567070, ...
          0.0101755746567070, ...
          0.0101755746567070, ...
          0.0101755746567070, ...
          0.0101755746567070, ...
          0.0101755746567070, ...
          0.0010653612328293, ...
          0.0010653612328293, ...
          0.0010653612328293, ...
          0.0252530603230362 ];

  return
end
