The dome

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An arch rotated about its vertical axis, and therefore a surface rather than a line. The rotation changes the behaviour in one important way: alongside the compression running down the meridians, the horizontal rings of the shell (the hoop direction) carry force too - compressive near the crown, tensile lower down. That hoop tension is why masonry domes crack radially near their base almost as a rule, and why builders girdle them with iron chains, thicken them into a drum, bury them in stepped rings of masonry, or accept the cracks and watch them. A dome also concentrates its outward thrust onto whatever it sits on, so the real design problem is rarely the shell and almost always the supports. Domes were built long before anyone could calculate any of this; the mathematics of shell behaviour arrives in the 18th century and after, many centuries later than the buildings.