function [ x, y, z, w ] = rule05 ( )

%*****************************************************************************80
%
%% rule05() returns the rule of precision 5.
%
%  Discussion:
%
%    The data is given for the following triangle:
%
%     (0,1) 
%       |   \ 
%       |    \ 
%       |     \ 
%       |      \ 
%     (0,0)----(1,0)
%
%  Licensing:
%
%    This code is distributed under the MIT license.
%
%  Modified:
%
%    23 April 2023
%
%  Author:
%
%    John Burkardt
%
%  Reference:
%
%    Freddie Witherden, Peter Vincent,
%    On the identification of symmetric quadrature rules for finite element methods,
%    Computers and Mathematics with Applications,
%    Volume 69, pages 1232-1241, 2015.
%
%  Output:
%
%    real x(n), y(n), z(n): the barycentric coordinates of quadrature points.
%
%    real w(n): the quadrature weights.
%
  x = [ ...
      0.3333333333333334, ...
      0.1012865073234563, ...
      0.7974269853530873, ...
      0.1012865073234563, ...
      0.4701420641051151, ...
      0.0597158717897698, ...
      0.4701420641051151 ];

  y = [ ...
      0.3333333333333334, ...
      0.7974269853530873, ...
      0.1012865073234563, ...
      0.1012865073234563, ...
      0.0597158717897698, ...
      0.4701420641051151, ...
      0.4701420641051151 ];

  z = [ ...
      0.3333333333333333, ...
      0.1012865073234563, ...
      0.1012865073234563, ...
      0.7974269853530873, ...
      0.4701420641051151, ...
      0.4701420641051150, ...
      0.0597158717897698 ];

  w = [ ...
      0.1125000000000000, ...
      0.0629695902724136, ...
      0.0629695902724136, ...
      0.0629695902724136, ...
      0.0661970763942531, ...
      0.0661970763942531, ...
      0.0661970763942531 ];
%
%  The weights should sum to 1, not 1/2!
%
  w = w * 2.0;

  return
end
