Left panel: twelve squares corresponding to the faces of the HEALPix framework (see Fig. 1) arranged as a net in the plane. The areas that are covered by multiple of the extended faces – the transition zones – are displayed in gray. The areas where pixels are “missing” are displayed in red. Right panel: six extended faces produced by the patchwork procedure. The two polar faces form the top row, followed by the four equatorial faces below. The shaded area around the transition zone of each composite face indicates the margin, which is later discarded.