function [ n, x, y, w, s ] = hexagon_rule_lyness06 ( )

%*****************************************************************************80
%
%% hexagon_rule_lyness06 sets the Lyness hexagon quadrature rule #06.
%
%  Licensing:
%
%    This code is distributed under the GNU LGPL license. 
%
%  Modified:
%
%    21 April 2019
%
%  Author:
%
%    John Burkardt
%
%  Reference:
%
%    James Lyness, Giovanni Monegato,
%    Quadrature rules for regions having regular hexagonal symmetry,
%    SIAM Journal on Numerical Analysis.
%    Volume 14 Number 2, April 1977, pages 283-295.
%
%  Parameters:
%
%    Output, integer n, the number of points.
%
%    Output, real x(n), y(n), the points.
%
%    Output, real w(n), the weights.
%
%    Output, integer s, the strength.
%
  n = 13;
  x = zeros ( n, 1 );
  y = zeros ( n, 1 );
  w = zeros ( n, 1 );
  
  x(1) = 0.0;
  y(1) = 0.0;
  w(1) = 0.2028525397412004;

  x(2) = 1.093286156810559;
  y(2) = 0.0000000000000000;
  w(2) = 0.03293968427506938 / 6.0;
  for i = 3 : 7
    x(i) = cosd ( 60.0 ) * x(i-1) - sind ( 60.0 ) * y(i-1);
    y(i) = sind ( 60.0 ) * x(i-1) + cosd ( 60.0 ) * y(i-1);
    w(i) = w(i-1);
  end

  x(8) = 0.6085065489767474;
  y(8) = 0.3513214198553754;
  w(8) = 0.7642077759837302 / 6.0;
  for i = 9 : 13
    x(i) = cosd ( 60.0 ) * x(i-1) - sind ( 60.0 ) * y(i-1);
    y(i) = sind ( 60.0 ) * x(i-1) + cosd ( 60.0 ) * y(i-1);
    w(i) = w(i-1);
  end

  s = 7;

  return
end
