Arinyo, Robert Juan2014-10-212014-10-2119951467-8659https://doi.org/10.1111/1467-8659.1450281We consider the problem of converting boundary representations of isothetic polyhedra into constructive solid geometry (CSG) representations. The CSG representation is a boolean formula based on the half-spaces supporting the faces of the polyhedron. This boolean formula exhibits two important features: no term is complemented (it is monotone) and each supporting half-space appears in the formula once and only once. It is known that such formulas do not always exist for general polyhedra in the three-dimensional space. In this work first we give a procedure that extends the domain of polyhedra for which such a nice representation can be computed. Then we prove that not all cyclic isothetic polyhedra have a CSG representation of the style given above.10.1111/1467-8659.1450281281-293