function [ a, b, c, d, w ] = rule12 ( )

%*****************************************************************************80
%
%% rule12() returns the rule of precision 12.
%
%  Licensing:
%
%    This code is distributed under the MIT license.
%
%  Modified:
%
%    02 April 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:
%
%    a(n), b(n), c(n), d(n): the barycentric coordinates of quadrature points.
%
%    w(n): the quadrature weights.
%
  a = [ ...
      0.21356799445330179599, ...
      0.35929601664009458428, ...
      0.21356799445330179599, ...
      0.21356799445330179599, ...
      0.08080469951147342678, ...
      0.75758590146557969192, ...
      0.08080469951147342678, ...
      0.08080469951147342678, ...
      0.14608946852754853274, ...
      0.56173159441735442954, ...
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      0.06406537703779889570, ...
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      0.69403517727214536492, ...
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      0.27633537059295731897, ...
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      0.69403517727214536492, ...
      0.01481472606744864938, ...
      0.00057879438757249416, ...
      0.04406791967562979917, ...
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      0.91128536626116796171, ...
      0.91128536626116796171, ...
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      0.04406791967562979917, ...
      0.00057879438757249416, ...
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      0.00057879438757249416, ...
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      0.79278383647296557513, ...
      0.02900481455515819401, ...
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      0.14920653441671805073, ...
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      0.39373386599840531908, ...
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      0.05001810761518710180, ...
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      0.03608735666657864050, ...
      0.03608735666657864050, ...
      0.11352723185190768951, ...
      0.25183678242711160511 ];

  b = [ ...
      0.21356799445330179599, ...
      0.21356799445330179599, ...
      0.35929601664009458428, ...
      0.21356799445330179599, ...
      0.08080469951147342678, ...
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      0.75758590146557969192, ...
      0.08080469951147342678, ...
      0.14608946852754853274, ...
      0.14608946852754853274, ...
      0.56173159441735442954, ...
      0.14608946852754853274, ...
      0.43593462296220109042, ...
      0.06406537703779889570, ...
      0.06406537703779889570, ...
      0.43593462296220109042, ...
      0.43593462296220109042, ...
      0.06406537703779889570, ...
      0.37238169507539831127, ...
      0.12761830492460168873, ...
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      0.37238169507539831127, ...
      0.37238169507539831127, ...
      0.12761830492460168873, ...
      0.01481472606744864938, ...
      0.69403517727214536492, ...
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      0.69403517727214536492, ...
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      0.27633537059295731897, ...
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      0.69403517727214536492, ...
      0.04406791967562979917, ...
      0.00057879438757249416, ...
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      0.00057879438757249416, ...
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      0.91128536626116796171, ...
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  c = [ ...
      0.21356799445330179599, ...
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end
