Soffit is the term, in architecture, given to the underside of any constructional feature; as for instance that of an arch or an architrave whether supported by piers or columns; also to the underside of a flight of stairs, and in the classic entablature to the underside of the projecting cornice.
Fascia: Fascia is the term in architechtuire for the board which runs along the ends of the rafters of a building and to which the guttering is fixed.
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Eavestroughs and Downpipes: Eavestroughs are the narrow channels which run along the eaves of a building and serves to collect rain water and direct it down away from the roof to prevent drips off the roof edges. Downpipes serve to direct the collected water to be drained away from the building