function [ a, b, c, w ] = rule05 ( )

%*****************************************************************************80
%
%% rule05() returns the rule of precision 5.
%
%  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 = [ ...
          0.1012865073234563, ...
          0.7974269853530872, ...
          0.1012865073234565, ...
          0.4701420641051151, ...
          0.4701420641051151, ...
          0.0597158717897698, ...
          0.3333333333333333 ];

  b = [ ...
          0.1012865073234565, ...
          0.1012865073234562, ...
          0.7974269853530874, ...
          0.0597158717897699, ...
          0.4701420641051151, ...
          0.4701420641051153, ...
          0.3333333333333334 ];

  c = [ ...
          0.7974269853530873, ...
          0.1012865073234566, ...
          0.1012865073234560, ...
          0.4701420641051151, ...
          0.0597158717897698, ...
          0.4701420641051149, ...
          0.3333333333333333 ];

  w = [ ...
          0.1259391805448272, ...
          0.1259391805448272, ...
          0.1259391805448272, ...
          0.1323941527885062, ...
          0.1323941527885062, ...
          0.1323941527885062, ...
          0.2250000000000000 ];

  return
end
