The new high-speed train station in Avignon, France, has a torus shape aligned to follow the natural lie of the land, with the main bulk of the building running East-West. The north facade is transparent glass while the south facade is clad in opaque aluminium panels.
The two geometrical surfaces defining the built volume that is the station are essentially two different-shaped, vertical axis toruses. (A torus is that surface or solid generated by the rotation of a circle about an axis outside its centre but lying on the same plane). The different surfaces described form the north and south facades respectively whereas the point at which the two toruses intersect forms the ridge of the building.
The two facades are clad with panels whose shape follows the family of curves described on the torus surfaces. Indeed, the lines generated by the basic torus shapes are a leitmotiv repeated throughout.
The parallels or circles are generated from the intersection of the torus surfaces and the planes perpendicular to the axis of that torus. The facets thus formed by these parallels are conical in shape and gradually change.
The meridians are generated by the intersection of the torus surfaces with the planes containing the axis of the torus. These meridians create a series of graduated cylindrical-shaped facets with an elliptical base on the surface of the torus. In contrast, the facets defined by the intersection of  meridians and parallels are flat.
The vertical section of the transparent north facade is “Z” shaped. Its external points are located on a torus with a radius of 17m while the internal points are on a torus generated by  a radius of 16.8m. The glazing is therefore contained within the space intervening between these two torus surfaces. The glass blocks are mounted on a linear frame of arches. The point supports at the overlaps of the glass panels serve also as spacers. The torus or space described by these arched mullions is the reference plane for the geometrical and practical assembly of the facade.
The opaque south-facing facade is completely clad in aluminium panels mounted on a similar structure to its north-facing counterpart. The internal surfacing is mounted on a separate support frame. Since only two toruses intersect to form the ridge or crown of the building, it follows that the internal surface plane of the opaque southern side is not a geometrical torus.
The lines “parallel to the ridge” are by definition parallel to their respective torus surface. This means that the internal side of the glass panels is not parallel to the outer plane. However, this non-alignment is less than the admissible tolerance for construction work and hence negligible. As the panels are rectangular, their edges cut through the plane of the arc at various angles depending on their position on the facade. Furthermore the surface described by the internal and external parallels or circles is not flat. As a result, the rectangular glass panels (maximum length 3m) had to be slightly cut away to comply with the overall geometry of the facade.
In order to maintain alignment with the “lines parallel to the ridge”, the truss beams on the internal and external cladding frames had to be placed at a constant angle to the perpendicular of the framework arch. To ensure this, the truss beams have been curved in the two directions to follow the geometry of the torus, and adjusted in order to obtain a constant angle.