function [ x, y, z, w ] = rule11 ( )

%*****************************************************************************80
%
%% rule11() returns the hexahedron rule of precision 11.
%
%  Discussion:
%
%    We suppose we are given a hexahedron H with vertices
%    (0,0,0), (1,0,0), (1,1,0), (0,1,0), (0,0,1), (1,0,1), (1,1,1), (0,1,1),
%    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 H is 
%    approximated by Q as follows:
%
%    Q = volume(H) * sum ( 1 <= i <= n ) w(i) * f(x(i),y(i),z(i)) 
%
%  Licensing:
%
%    This code is distributed under the MIT license.
%
%  Modified:
%
%    01 May 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 coordinates of quadrature points.
%
%    real w(n): the quadrature weights, which sum to 1.
%
  x = [ ...
          0.0936928329501868, ...
          0.5000000000000000, ...
          0.5000000000000000, ...
          0.5000000000000000, ...
          0.9063071670498133, ...
          0.5000000000000000, ...
          0.8008376320991313, ...
          0.1991623679008687, ...
          0.1991623679008687, ...
          0.1991623679008687, ...
          0.1991623679008687, ...
          0.8008376320991313, ...
          0.8008376320991313, ...
          0.8008376320991313, ...
          0.9277278805088800, ...
          0.0722721194911200, ...
          0.0722721194911200, ...
          0.0722721194911200, ...
          0.0722721194911200, ...
          0.9277278805088800, ...
          0.9277278805088800, ...
          0.9277278805088800, ...
          0.6566967022580273, ...
          0.3433032977419727, ...
          0.3433032977419727, ...
          0.3433032977419727, ...
          0.3433032977419727, ...
          0.6566967022580273, ...
          0.6566967022580273, ...
          0.6566967022580273, ...
          0.1326658565014960, ...
          0.8673341434985040, ...
          0.5000000000000000, ...
          0.8673341434985040, ...
          0.8673341434985040, ...
          0.5000000000000000, ...
          0.5000000000000000, ...
          0.1326658565014960, ...
          0.1326658565014960, ...
          0.8673341434985040, ...
          0.5000000000000000, ...
          0.1326658565014960, ...
          0.7253999675572547, ...
          0.2746000324427453, ...
          0.2746000324427453, ...
          0.0174501672436448, ...
          0.2746000324427453, ...
          0.9825498327563551, ...
          0.7253999675572547, ...
          0.7253999675572547, ...
          0.2746000324427453, ...
          0.7253999675572547, ...
          0.0174501672436448, ...
          0.2746000324427453, ...
          0.2746000324427453, ...
          0.2746000324427453, ...
          0.7253999675572547, ...
          0.9825498327563551, ...
          0.7253999675572547, ...
          0.9825498327563551, ...
          0.9825498327563551, ...
          0.0174501672436448, ...
          0.7253999675572547, ...
          0.2746000324427453, ...
          0.7253999675572547, ...
          0.0174501672436448, ...
          0.9706224286053016, ...
          0.0293775713946984, ...
          0.0293775713946984, ...
          0.3230485927016850, ...
          0.0293775713946984, ...
          0.6769514072983150, ...
          0.9706224286053016, ...
          0.9706224286053016, ...
          0.0293775713946984, ...
          0.9706224286053016, ...
          0.3230485927016850, ...
          0.0293775713946984, ...
          0.0293775713946984, ...
          0.0293775713946984, ...
          0.9706224286053016, ...
          0.6769514072983150, ...
          0.9706224286053016, ...
          0.6769514072983150, ...
          0.6769514072983150, ...
          0.3230485927016850, ...
          0.9706224286053016, ...
          0.0293775713946984, ...
          0.9706224286053016, ...
          0.3230485927016850 ];

  y = [ ...
          0.5000000000000000, ...
          0.5000000000000000, ...
          0.9063071670498133, ...
          0.5000000000000000, ...
          0.5000000000000000, ...
          0.0936928329501868, ...
          0.1991623679008687, ...
          0.8008376320991313, ...
          0.8008376320991313, ...
          0.1991623679008687, ...
          0.1991623679008687, ...
          0.8008376320991313, ...
          0.8008376320991313, ...
          0.1991623679008687, ...
          0.0722721194911200, ...
          0.9277278805088800, ...
          0.9277278805088800, ...
          0.0722721194911200, ...
          0.0722721194911200, ...
          0.9277278805088800, ...
          0.9277278805088800, ...
          0.0722721194911200, ...
          0.3433032977419727, ...
          0.6566967022580273, ...
          0.6566967022580273, ...
          0.3433032977419727, ...
          0.3433032977419727, ...
          0.6566967022580273, ...
          0.6566967022580273, ...
          0.3433032977419727, ...
          0.1326658565014960, ...
          0.5000000000000000, ...
          0.8673341434985040, ...
          0.8673341434985040, ...
          0.5000000000000000, ...
          0.1326658565014960, ...
          0.1326658565014960, ...
          0.5000000000000000, ...
          0.8673341434985040, ...
          0.1326658565014960, ...
          0.8673341434985040, ...
          0.5000000000000000, ...
          0.9825498327563551, ...
          0.0174501672436448, ...
          0.9825498327563551, ...
          0.2746000324427453, ...
          0.2746000324427453, ...
          0.7253999675572547, ...
          0.0174501672436448, ...
          0.0174501672436448, ...
          0.0174501672436448, ...
          0.7253999675572547, ...
          0.7253999675572547, ...
          0.7253999675572547, ...
          0.7253999675572547, ...
          0.2746000324427453, ...
          0.2746000324427453, ...
          0.2746000324427453, ...
          0.9825498327563551, ...
          0.7253999675572547, ...
          0.2746000324427453, ...
          0.7253999675572547, ...
          0.7253999675572547, ...
          0.9825498327563551, ...
          0.2746000324427453, ...
          0.2746000324427453, ...
          0.6769514072983150, ...
          0.3230485927016850, ...
          0.6769514072983150, ...
          0.0293775713946984, ...
          0.0293775713946984, ...
          0.9706224286053016, ...
          0.3230485927016850, ...
          0.3230485927016850, ...
          0.3230485927016850, ...
          0.9706224286053016, ...
          0.9706224286053016, ...
          0.9706224286053016, ...
          0.9706224286053016, ...
          0.0293775713946984, ...
          0.0293775713946984, ...
          0.0293775713946984, ...
          0.6769514072983150, ...
          0.9706224286053016, ...
          0.0293775713946984, ...
          0.9706224286053016, ...
          0.9706224286053016, ...
          0.6769514072983150, ...
          0.0293775713946984, ...
          0.0293775713946984 ];

  z = [ ...
          0.5000000000000000, ...
          0.9063071670498133, ...
          0.5000000000000000, ...
          0.0936928329501868, ...
          0.5000000000000000, ...
          0.5000000000000000, ...
          0.1991623679008687, ...
          0.8008376320991313, ...
          0.1991623679008687, ...
          0.1991623679008687, ...
          0.8008376320991313, ...
          0.1991623679008687, ...
          0.8008376320991313, ...
          0.8008376320991313, ...
          0.0722721194911200, ...
          0.9277278805088800, ...
          0.0722721194911200, ...
          0.0722721194911200, ...
          0.9277278805088800, ...
          0.0722721194911200, ...
          0.9277278805088800, ...
          0.9277278805088800, ...
          0.3433032977419727, ...
          0.6566967022580273, ...
          0.3433032977419727, ...
          0.3433032977419727, ...
          0.6566967022580273, ...
          0.3433032977419727, ...
          0.6566967022580273, ...
          0.6566967022580273, ...
          0.5000000000000000, ...
          0.1326658565014960, ...
          0.1326658565014960, ...
          0.5000000000000000, ...
          0.8673341434985040, ...
          0.8673341434985040, ...
          0.1326658565014960, ...
          0.8673341434985040, ...
          0.5000000000000000, ...
          0.5000000000000000, ...
          0.8673341434985040, ...
          0.1326658565014960, ...
          0.2746000324427453, ...
          0.7253999675572547, ...
          0.2746000324427453, ...
          0.7253999675572547, ...
          0.9825498327563551, ...
          0.2746000324427453, ...
          0.2746000324427453, ...
          0.7253999675572547, ...
          0.2746000324427453, ...
          0.0174501672436448, ...
          0.2746000324427453, ...
          0.0174501672436448, ...
          0.9825498327563551, ...
          0.0174501672436448, ...
          0.9825498327563551, ...
          0.2746000324427453, ...
          0.7253999675572547, ...
          0.7253999675572547, ...
          0.7253999675572547, ...
          0.7253999675572547, ...
          0.9825498327563551, ...
          0.7253999675572547, ...
          0.0174501672436448, ...
          0.2746000324427453, ...
          0.0293775713946984, ...
          0.9706224286053016, ...
          0.0293775713946984, ...
          0.9706224286053016, ...
          0.6769514072983150, ...
          0.0293775713946984, ...
          0.0293775713946984, ...
          0.9706224286053016, ...
          0.0293775713946984, ...
          0.3230485927016850, ...
          0.0293775713946984, ...
          0.3230485927016850, ...
          0.6769514072983150, ...
          0.3230485927016850, ...
          0.6769514072983150, ...
          0.0293775713946984, ...
          0.9706224286053016, ...
          0.9706224286053016, ...
          0.9706224286053016, ...
          0.9706224286053016, ...
          0.6769514072983150, ...
          0.9706224286053016, ...
          0.3230485927016850, ...
          0.0293775713946984 ];

  w = [ ...
          0.0253096342016000, ...
          0.0253096342016000, ...
          0.0253096342016000, ...
          0.0253096342016000, ...
          0.0253096342016000, ...
          0.0253096342016000, ...
          0.0146922934945570, ...
          0.0146922934945570, ...
          0.0146922934945570, ...
          0.0146922934945570, ...
          0.0146922934945570, ...
          0.0146922934945570, ...
          0.0146922934945570, ...
          0.0146922934945570, ...
          0.0055804890098537, ...
          0.0055804890098537, ...
          0.0055804890098537, ...
          0.0055804890098537, ...
          0.0055804890098537, ...
          0.0055804890098537, ...
          0.0055804890098537, ...
          0.0055804890098537, ...
          0.0269990056568711, ...
          0.0269990056568711, ...
          0.0269990056568711, ...
          0.0269990056568711, ...
          0.0269990056568711, ...
          0.0269990056568711, ...
          0.0269990056568711, ...
          0.0269990056568711, ...
          0.0181499182325145, ...
          0.0181499182325145, ...
          0.0181499182325145, ...
          0.0181499182325145, ...
          0.0181499182325145, ...
          0.0181499182325145, ...
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          0.0181499182325145, ...
          0.0181499182325145, ...
          0.0181499182325145, ...
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          0.0181499182325145, ...
          0.0076802492622294, ...
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          0.0028267870173527, ...
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          0.0028267870173527, ...
          0.0028267870173527, ...
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          0.0028267870173527 ];

  return
end
