A striped lining inside a dome is a geometry problem: the stripes have to radiate from the crown, which means every panel is a wedge, and every wedge is a different size.
The dome is set out as a series of segments running from the crown down to the arm line, like the gores of an umbrella. Each segment is wider at the bottom than the top, so a straight-cut stripe would fan sideways as it descended. Instead, each panel is cut so its stripes run along the centre line of that segment, and the seams between panels are placed where two stripes meet - so the join disappears into the pattern rather than crossing it.
Our upholsterers cut a paper template for every segment from the finished timber frame rather than from the drawing, because the frame is shaped by hand and no two domes are dimensionally identical.
At the crown, where all the segments converge, the last few centimetres are covered by a stitched rosette. Every radiating pattern in upholstery ends in something covering its centre, for the same reason: geometry that converges to a point cannot be made to lie flat.