tree.insert(plusZPlane.span(), RegionCutRule.INHERIT);

            // create the vertices for the octahedron
            final double cx = center.getX();
            final double cy = center.getY();
            final double cz = center.getZ();

            final Vector3D maxX = Vector3D.of(cx + radius, cy, cz);
            final Vector3D minX = Vector3D.of(cx - radius, cy, cz);

            final Vector3D maxY = Vector3D.of(cx, cy + radius, cz);
            final Vector3D minY = Vector3D.of(cx, cy - radius, cz);

            final Vector3D maxZ = Vector3D.of(cx, cy, cz + radius);
            final Vector3D minZ = Vector3D.of(cx, cy, cz - radius);