The wedge in Minkowski space has the property that its space-like complement of this set coincides with the reflection at the origin of this set. This implies that the commutant of the von Neumann algebra associated with the wedge coincides with the algebra associated with the opposite set. This geometric symmetry implies symmetries for Tomita’s modular theory also. If one defines sub-algebras of the double cones or cylinders by intersecting the algebras of the shifted wedges, one can re-construct the algebras of the larger double-cones or the wedge with help of either the translations or the modular group of the wedge-algebra. The symmetry of the wedge and its algebra implies by simple arguments the von Neumann algebra of the wedge is of type III. By a careful look at Connes’ definition of the classification of the type III-algebras we will show that this algebra is of Connes-type III1 . By the same method we will find that also the von Neumann algebras of double-cones are of Connes-type III1 .