AbstractA floating-point arithmetic algorithm designed for solving usual boolean operations (intersection, union, and difference) on arbitrary polyhedral meshes is described in this paper. It can be used in many pre- and post-processing applications in computational physics (e.g. cut-cell volume mesh generation or high order conservative remapping). The method provides conformal polyhedral meshes upon exit. The core idea is to triangulate the polygons, solve the intersections at the triangular level, reconstruct the polyhedra from the cloud of conformal triangles and then re-aggregate their triangular faces to polygons. This approach offers a great flexibility regarding the admissible topologies: non-planar faces, concave faces or cells and some non-manifoldness are handled. The algorithm is described in details and some preliminary results are shown.