Unlike an arch, a dome can be thought of as a thin shell, with forces acting smoothly within its surface. It is then treated as if the minimum thickness is set mainly to avoid local buckling. The compressive stress required to support the dome is independent of the thickness, for the dome as for other thin shells, such as cones. However, the thickness is often combined with the stress in the ‘stress resultant’ of membrane techniques. The techniques demonstrate that tensile stresses can develop near the base of the dome. If its supports move, a hemispherical dome can crack into orange-like segments along lines from its base towards its crown. It can be assembled from such notional segments. Opposite segments paired at their crown as ‘arches’ can be analysed separately to find the minimum thickness. From the use of ‘arches’ for complete domes comes the use of slices for incomplete domes, which have lost some adjacent segments. The results show that complete domes can be thinner than incomplete ones. There remain difficulties, though: in a dome that has (say) eight sides, stresses focussed on the ribs between the sides need analysis.