Christmas tree pests and weeds of different pests, most of which cause cosmetic damage to the trees, important in the Christmas tree industry. The balsam woolly adelgid ("Adelges picae") are small soft-bodied insects which attack the Fraser fir. The insects appear as white, woolly spots on the tree and are fatal to the fir if left untreated. The woolly adeligid was native to central Europe where it affected the silver fir; it was introduced to the United States, where it has no known native predators, before 1900. Balsam twig aphids ("Mindarus abietnus") are another type of tree pest which affects fir and spruce trees in
Noble polyhedron 'dual' covers both kinds. The dual of a noble polyhedron is also noble. Many are also self-dual: Noble polyhedron A noble polyhedron is one which is isohedral (all faces the same) and isogonal (all vertices the same). They were first studied in any depth by Hess and Bruckner in late 19th century, and later by Grünbaum. There are four main classes of noble polyhedra: If we allow some of Grünbaum's stranger constructions as polyhedra, then we have two more infinite series of toroids: We can distinguish between dual structural forms (topologies) on the one hand, and dual geometrical arrangements when