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

%*****************************************************************************80
%
%% rule06() returns the prism rule of precision 6.
%
%  Discussion:
%
%    We suppose we are given a triangular prism P with vertices
%    (1,0,0), (0,1,0), (0,0,0),
%    (1,0,1), (0,1,1), (0,0,1),
%    We call a rule with n points, returning coordinates
%    x, y, z, and weights w.  Then the integral I of f(x,y,z) over P is 
%    approximated by Q as follows:
%
%    Q = volume(P) * sum ( 1 <= i <= n ) w(i) * f(x(i),y(i),z(i)) 
%
%  Licensing:
%
%    This code is distributed under the MIT license.
%
%  Modified:
%
%    02 May 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:
%
%    real x(n), y(n), z(n): the coordinates of quadrature points.
%
%    real w(n): the quadrature weights, which sum to 1.
%
  x = [ ...
          0.3333333333333333, ...
          0.3333333333333333, ...
          0.3333333333333333, ...
          0.3333333333333333, ...
          0.0175042446586512, ...
          0.0175042446586512, ...
          0.9649915106826975, ...
          0.1617417813899514, ...
          0.1617417813899514, ...
          0.6765164372200974, ...
          0.4656535513495914, ...
          0.4656535513495914, ...
          0.0686928973008173, ...
          0.4656535513495914, ...
          0.4656535513495914, ...
          0.0686928973008173, ...
          0.0345948698524570, ...
          0.2025039451729335, ...
          0.0345948698524570, ...
          0.7629011849746096, ...
          0.2025039451729335, ...
          0.7629011849746096, ...
          0.0345948698524570, ...
          0.2025039451729335, ...
          0.0345948698524570, ...
          0.7629011849746096, ...
          0.2025039451729335, ...
          0.7629011849746096 ];

  y = [ ...
          0.3333333333333333, ...
          0.3333333333333333, ...
          0.3333333333333333, ...
          0.3333333333333333, ...
          0.0175042446586512, ...
          0.9649915106826975, ...
          0.0175042446586512, ...
          0.1617417813899514, ...
          0.6765164372200974, ...
          0.1617417813899514, ...
          0.4656535513495914, ...
          0.0686928973008173, ...
          0.4656535513495914, ...
          0.4656535513495914, ...
          0.0686928973008173, ...
          0.4656535513495914, ...
          0.2025039451729335, ...
          0.0345948698524570, ...
          0.7629011849746096, ...
          0.0345948698524570, ...
          0.7629011849746096, ...
          0.2025039451729335, ...
          0.2025039451729335, ...
          0.0345948698524570, ...
          0.7629011849746096, ...
          0.0345948698524570, ...
          0.7629011849746096, ...
          0.2025039451729335 ];

  z = [ ...
          0.9925192962207799, ...
          0.0074807037792201, ...
          0.2480010523941030, ...
          0.7519989476058970, ...
          0.5000000000000000, ...
          0.5000000000000000, ...
          0.5000000000000000, ...
          0.5000000000000000, ...
          0.5000000000000000, ...
          0.5000000000000000, ...
          0.7405713004233492, ...
          0.7405713004233492, ...
          0.7405713004233492, ...
          0.2594286995766508, ...
          0.2594286995766508, ...
          0.2594286995766508, ...
          0.0952682547954233, ...
          0.0952682547954233, ...
          0.0952682547954233, ...
          0.0952682547954233, ...
          0.0952682547954233, ...
          0.0952682547954233, ...
          0.9047317452045767, ...
          0.9047317452045767, ...
          0.9047317452045767, ...
          0.9047317452045767, ...
          0.9047317452045767, ...
          0.9047317452045767 ];

  w = [ ...
          0.0361446293820950, ...
          0.0361446293820950, ...
          0.0554469020242208, ...
          0.0554469020242208, ...
          0.0116429635765844, ...
          0.0116429635765844, ...
          0.0116429635765844, ...
          0.0768806419265571, ...
          0.0768806419265571, ...
          0.0768806419265571, ...
          0.0496268551496232, ...
          0.0496268551496232, ...
          0.0496268551496232, ...
          0.0496268551496232, ...
          0.0496268551496232, ...
          0.0496268551496232, ...
          0.0211237491483504, ...
          0.0211237491483504, ...
          0.0211237491483504, ...
          0.0211237491483504, ...
          0.0211237491483504, ...
          0.0211237491483504, ...
          0.0211237491483504, ...
          0.0211237491483504, ...
          0.0211237491483504, ...
          0.0211237491483504, ...
          0.0211237491483504, ...
          0.0211237491483504 ];

  return
end
