function [ x, y, z, w ] = rule06 ( )

%*****************************************************************************80
%
%% rule06() returns the rule of precision 6.
%
%  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 = [ ...
      0.0630890144915022, ...
      0.8738219710169955, ...
      0.0630890144915022, ...
      0.2492867451709104, ...
      0.5014265096581791, ...
      0.2492867451709104, ...
      0.0531450498448169, ...
      0.6365024991213987, ...
      0.3103524510337844, ...
      0.6365024991213987, ...
      0.3103524510337844, ...
      0.0531450498448169 ];

  y = [ ...
      0.8738219710169955, ...
      0.0630890144915022, ...
      0.0630890144915022, ...
      0.5014265096581791, ...
      0.2492867451709104, ...
      0.2492867451709104, ...
      0.6365024991213987, ...
      0.0531450498448169, ...
      0.6365024991213987, ...
      0.3103524510337844, ...
      0.0531450498448169, ...
      0.3103524510337844 ];

  z = [ ...
      0.0630890144915023, ...
      0.0630890144915022, ...
      0.8738219710169957, ...
      0.2492867451709104, ...
      0.2492867451709104, ...
      0.5014265096581791, ...
      0.3103524510337844, ...
      0.3103524510337844, ...
      0.0531450498448169, ...
      0.0531450498448169, ...
      0.6365024991213987, ...
      0.6365024991213987 ];

  w = [ ...
      0.0254224531851034, ...
      0.0254224531851034, ...
      0.0254224531851034, ...
      0.0583931378631897, ...
      0.0583931378631897, ...
      0.0583931378631897, ...
      0.0414255378091868, ...
      0.0414255378091868, ...
      0.0414255378091868, ...
      0.0414255378091868, ...
      0.0414255378091868, ...
      0.0414255378091868 ];
%
%  The weights should sum to 1, not 1/2!
%
  w = w * 2.0;

  return
end
