A fan back is upholstery pretending to be geometry, and it only works if the pleats radiate from a single point.
That point sits below the seat line, outside the panel altogether - which means every pleat in the fan is at a different angle from its neighbour, and each one has to be laid to a line struck from that imaginary centre rather than folded by eye.
So our upholsterers strike the radiating lines onto the frame first, from a compass point marked on the workshop floor, and each pleat is pulled to its own line. The fullness of cloth in each pleat is also graduated - more at the top of the fan where the arc is wider, less at the base where the pleats converge - so the folds appear to be the same width all the way up when they are in fact tapering.
The carved frame around the fan is then fitted to the finished upholstery rather than the other way round, so that the silvered scrollwork lands exactly on the edge of the pleating with no gap for the eye to find.