function [ x, y, z, w ] = rule11 ( )

%*****************************************************************************80
%
%% rule11() returns the prism rule of precision 11.
%
%  Discussion:
%
%    We suppose we are given a triangular prism P with vertices
%    (1,0,0), (0,1,0), (0,0,0),
%    (1,0,1), (0,1,1), (0,0,1),
%    We call a rule with n points, returning coordinates
%    x, y, z, and weights w.  Then the integral I of f(x,y,z) over P is 
%    approximated by Q as follows:
%
%    Q = volume(P) * sum ( 1 <= i <= n ) w(i) * f(x(i),y(i),z(i)) 
%
%  Licensing:
%
%    This code is distributed under the MIT license.
%
%  Modified:
%
%    02 May 2023
%
%  Author:
%
%    John Burkardt
%
%  Reference:
%
%    Jan Jaskowiec, Natarajan Sukumar,
%    High order symmetric cubature rules for tetrahedra and pyramids,
%    International Journal of Numerical Methods in Engineering,
%    Volume 122, Number 1, pages 148-171, 24 August 2020.
%
%  Output:
%
%    real x(n), y(n), z(n): the coordinates of quadrature points.
%
%    real w(n): the quadrature weights, which sum to 1.
%
  x = [ ...
          0.3333333333333333, ...
          0.3333333333333333, ...
          0.3333333333333333, ...
          0.3333333333333333, ...
          0.3333333333333333, ...
          0.3333333333333333, ...
          0.4269221881685347, ...
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          0.1461556236629306, ...
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  y = [ ...
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          0.3333333333333333, ...
          0.4269221881685347, ...
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          0.4396327659106838, ...
          0.1207344681786323, ...
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          0.4396327659106838, ...
          0.2009128761138035, ...
          0.5981742477723929, ...
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          0.9568298039136461, ...
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          0.9568298039136461, ...
          0.0215850980431769, ...
          0.4941546402080231, ...
          0.0116907195839538, ...
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          0.4941546402080231, ...
          0.0116907195839538, ...
          0.4941546402080231, ...
          0.0599602772654436, ...
          0.8800794454691128, ...
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          0.0599602772654436, ...
          0.8800794454691128, ...
          0.0599602772654436, ...
          0.2328102236807494, ...
          0.5343795526385012, ...
          0.2328102236807494, ...
          0.2328102236807494, ...
          0.5343795526385012, ...
          0.2328102236807494, ...
          0.1213201391549184, ...
          0.7573597216901632, ...
          0.1213201391549184, ...
          0.1213201391549184, ...
          0.7573597216901632, ...
          0.1213201391549184, ...
          0.4987543911906001, ...
          0.0024912176187997, ...
          0.4987543911906001, ...
          0.4987543911906001, ...
          0.0024912176187997, ...
          0.4987543911906001, ...
          0.0165184963342511, ...
          0.1046140524481813, ...
          0.8788674512175675, ...
          0.1046140524481813, ...
          0.8788674512175675, ...
          0.0165184963342511, ...
          0.2979854667459965, ...
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          0.6300512762784186, ...
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          0.6339787844594131, ...
          0.3197359768880742, ...
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          0.0462852386525127 ];

  z = [ ...
          0.2225225095750167, ...
          0.7774774904249833, ...
          0.9852161050240122, ...
          0.0147838949759878, ...
          0.4588747274117720, ...
          0.5411252725882280, ...
          0.5000000000000000, ...
          0.5000000000000000, ...
          0.5000000000000000, ...
          0.8379989630425995, ...
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          0.8379989630425995, ...
          0.1620010369574005, ...
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          0.9180267718000730, ...
          0.9180267718000730, ...
          0.9180267718000730, ...
          0.0819732281999270, ...
          0.0819732281999270, ...
          0.0819732281999270, ...
          0.7930952762440336, ...
          0.7930952762440336, ...
          0.7930952762440336, ...
          0.2069047237559664, ...
          0.2069047237559664, ...
          0.2069047237559664, ...
          0.9873500827745887, ...
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          0.9725136338749176, ...
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          0.2124923289596651, ...
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  w = [ ...
          0.0216801440673047, ...
          0.0216801440673047, ...
          0.0104576079858723, ...
          0.0104576079858723, ...
          0.0034934625077134, ...
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          0.0161061041817141, ...
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          0.0220331028546643, ...
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  return
end
