Vaults were built sometimes of brick, sometimes of cut stone; in a few cases even of earthenware jars fitting into each other, and laid up in a continuous contracting spiral from the base to the crown of a dome, as in San Vitale at Ravenna. Ingenious processes for building vaults without centrings were made use of--processes inherited from the drain-builders of ancient Assyria, and still in vogue in Armenia, Persia, and Asia Minor. The groined vault was common, but always approximated the form of a dome, by a longitudinal convexity upward in the intersecting vaults. The aisles of Hagia Sophia[17] display a remarkable variety of forms in the vaulting. [Footnote 17: “St. Sophia,” the common name of this church, is a misnomer. It was not dedicated to a saint at all, but to the Divine Wisdom (Hagia Sophia), which name the Turks have retained in the softened form “Aya Sofia.”] [Illustration: FIG. 71.--DIAGRAM OF PENDENTIVES.] +DOMES.+ The dome, as we have seen, early became the most characteristic feature of Byzantine architecture; and especially the dome on pendentives. If a hemisphere be cut by five planes, four perpendicular to its base and bounding a square inscribed therein, and the fifth plane parallel to the base and tangent to the semicircular intersections made by the first four, there will remain of the original surface only four triangular spaces bounded by arcs of circles. These are called _pendentives_ (Fig. 71 a). When these are built up of masonry, each course forms a species of arch, by virtue of its convexity. At the crown of the four arches on which they rest, these courses meet and form a complete circle, perfectly stable and capable of sustaining any superstructure that does not by excessive weight disrupt the whole fabric by overthrowing the four arches which support it. Upon these pendentives, then, a new dome may be started of any desired curvature, or even a cylindrical drum to support a still loftier dome, as in the later churches (Fig. 71 b). This method of covering a square is simpler than the groined vault, having no sharp edges or intersections; it is at least as effective architecturally, by reason of its greater height in the centre; and is equally applicable to successive bays of an oblong, cruciform, and even columnar building. In the great cisterns at Constantinople vast areas are covered by rows of small domes supported on ranges of columns.