Abstract: A holding device holds an optical component having an optical surface with a polygonal border and having a cylindrical substrate body with a cylinder lateral wall with a polygonal cross section corresponding to the border of the optical surface. The holding device has a holding frame. At least two bearing bodies of the holding device make bearing contact with the lateral wall of the substrate body by way of bearing portions of the lateral wall. At least one pressing body of the holding device exerts a bearing pressure that presses the substrate body against the bearing body. The holding device can securely hold optical components having an optical surface with a polygonal border and having a cylindrical substrate body and moreover enables positionally accurate mounting.