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

%*****************************************************************************80
%
%% rule06() returns the pyramid quadrature rule of precision 6.
%
%  Discussion:
%
%    We suppose we are given a pyramid P with vertices
%      (-1,-1,0), (-1,+1,0), (+1,+1,0), (+1,-1,0), (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:
%
%    25 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:
%
%    x(n), y(n), z(n): the coordinates of quadrature points.
%
%    w(n): the quadrature weights, which sum to 1.
%
  x = [ ...
          0.0000000000000000, ...
          0.0000000000000000, ...
          0.0000000000000000, ...
          0.0000000000000000, ...
          0.8345953511147084, ...
          0.0000000000000000, ...
         -0.8345953511147084, ...
          0.0000000000000000, ...
          0.4339254093766991, ...
          0.0000000000000000, ...
         -0.4339254093766991, ...
          0.0000000000000000, ...
          0.5656808544256755, ...
          0.5656808544256755, ...
         -0.5656808544256755, ...
         -0.5656808544256755, ...
          0.4980790917807059, ...
          0.4980790917807059, ...
         -0.4980790917807059, ...
         -0.4980790917807059, ...
          0.9508994872144825, ...
          0.9508994872144825, ...
         -0.9508994872144825, ...
         -0.9508994872144825 ];

  y = [ ...
          0.0000000000000000, ...
          0.0000000000000000, ...
          0.0000000000000000, ...
          0.0000000000000000, ...
          0.0000000000000000, ...
          0.8345953511147084, ...
          0.0000000000000000, ...
         -0.8345953511147084, ...
          0.0000000000000000, ...
          0.4339254093766991, ...
          0.0000000000000000, ...
         -0.4339254093766991, ...
          0.5656808544256755, ...
         -0.5656808544256755, ...
          0.5656808544256755, ...
         -0.5656808544256755, ...
          0.4980790917807059, ...
         -0.4980790917807059, ...
          0.4980790917807059, ...
         -0.4980790917807059, ...
          0.9508994872144825, ...
         -0.9508994872144825, ...
          0.9508994872144825, ...
         -0.9508994872144825 ];

  z = [ ...
          0.8076457976939595, ...
          0.0017638088528196, ...
          0.1382628064637306, ...
          0.4214239119356371, ...
          0.0974473410254620, ...
          0.0974473410254620, ...
          0.0974473410254620, ...
          0.0974473410254620, ...
          0.5660745906233009, ...
          0.5660745906233009, ...
          0.5660745906233009, ...
          0.5660745906233009, ...
          0.0294777308457207, ...
          0.0294777308457207, ...
          0.0294777308457207, ...
          0.0294777308457207, ...
          0.2649158632121295, ...
          0.2649158632121295, ...
          0.2649158632121295, ...
          0.2649158632121295, ...
          0.0482490706319360, ...
          0.0482490706319360, ...
          0.0482490706319360, ...
          0.0482490706319360 ];

  w = [ ...
          0.0254628936626420, ...
          0.0160535131751913, ...
          0.1195795544525238, ...
          0.1030606701991518, ...
          0.0369505879363295, ...
          0.0369505879363295, ...
          0.0369505879363295, ...
          0.0369505879363295, ...
          0.0315875794881733, ...
          0.0315875794881733, ...
          0.0315875794881733, ...
          0.0315875794881733, ...
          0.0372001293894483, ...
          0.0372001293894483, ...
          0.0372001293894483, ...
          0.0372001293894483, ...
          0.0738823846769269, ...
          0.0738823846769269, ...
          0.0738823846769269, ...
          0.0738823846769269, ...
          0.0043401606367449, ...
          0.0043401606367449, ...
          0.0043401606367449, ...
          0.0043401606367449 ];

  return
end
