function [ x, y, z, w ] = rule08 ( )

%*****************************************************************************80
%
%% rule08() returns the rule of precision 8.
%
%  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, ...
      0.4592925882927231, ...
      0.0814148234145537, ...
      0.4592925882927231, ...
      0.1705693077517602, ...
      0.6588613844964796, ...
      0.1705693077517602, ...
      0.0505472283170310, ...
      0.8989055433659381, ...
      0.0505472283170310, ...
      0.0083947774099576, ...
      0.7284923929554042, ...
      0.2631128296346381, ...
      0.7284923929554042, ...
      0.2631128296346381, ...
      0.0083947774099576 ];

  y = [ ...
      0.3333333333333334, ...
      0.0814148234145537, ...
      0.4592925882927231, ...
      0.4592925882927231, ...
      0.6588613844964796, ...
      0.1705693077517602, ...
      0.1705693077517602, ...
      0.8989055433659381, ...
      0.0505472283170310, ...
      0.0505472283170310, ...
      0.7284923929554042, ...
      0.0083947774099576, ...
      0.7284923929554042, ...
      0.2631128296346381, ...
      0.0083947774099576, ...
      0.2631128296346381 ];

  z = [ ...
      0.3333333333333333, ...
      0.4592925882927232, ...
      0.4592925882927231, ...
      0.0814148234145537, ...
      0.1705693077517602, ...
      0.1705693077517602, ...
      0.6588613844964795, ...
      0.0505472283170310, ...
      0.0505472283170310, ...
      0.8989055433659381, ...
      0.2631128296346382, ...
      0.2631128296346382, ...
      0.0083947774099576, ...
      0.0083947774099576, ...
      0.7284923929554044, ...
      0.7284923929554044 ];

  w = [ ...
      0.0721578038388936, ...
      0.0475458171336423, ...
      0.0475458171336423, ...
      0.0475458171336423, ...
      0.0516086852673591, ...
      0.0516086852673591, ...
      0.0516086852673591, ...
      0.0162292488115990, ...
      0.0162292488115990, ...
      0.0162292488115990, ...
      0.0136151570872175, ...
      0.0136151570872175, ...
      0.0136151570872175, ...
      0.0136151570872175, ...
      0.0136151570872175, ...
      0.0136151570872175 ];
%
%  The weights should sum to 1, not 1/2!
%
  w = w * 2.0;

  return
end
