  In this paper we provide a tetrahedra-free algorithm to compute
low-cardinality quadrature rules with a given degree of polynomial exactness,
positive weights and interior nodes on a polyhedral element with arbitrary
shape. The key tools are the notion of Tchakaloff discretization set and the
solution of moment-matching equations by Lawson-Hanson iterations for
NonNegative Least-Squares. Several numerical tests are presented. The method is
implemented in Matlab as open-source software.
