hexahedron_witherden_rule, an Octave code which returns a Witherden quadrature rule, with exactness up to total degree 11, over the interior of a hexahedron.

The unit hexahedron has 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).


The computer code and data files made available on this web page are distributed under the MIT license


hexahedron_witherden_rule is available in a C version and a C++ version and a Fortran90 version and a MATLAB version and an Octave version and a Python version.

Related Data and Programs:



  1. 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.

Source Code:

Last revised on 21 May 2023.