[....] The crossing vaults found a wide space in the treaty of Vandelvira (1580). The most interesting aspect of the models developed by Vandelvira is that all crossing vaults are pendentive vaults, that is spherical ones. This circumstance permits Vandelvira to propose, in the carving of his crossings, one geometric design based on the spherical domes stereotomy. If the crossing vault was spherical, as Vandelvira proposed, all the ribs that form the grid must have different curvatures (photo 3).

Nevertheless, we observed that, the real construction, of this kind of vaults usually is based in a most effective geometry, Frequently, the shape of the vault is the consequence of sliding the curvature of the perimeter arch by the two perpendicular ones. The surface obtained is not a sphere but a translation surface in which all its ribs have the same curvature. Here we have a new strategy in order to standardize the vault as completely as possible (photo 4).

As we can see here, quite often, the perimeter arches are oval arches which means, an arch that consists of three curves: the central curve and two smaller ones on its ends. Then, the central grid could be built with the same arch: the central part of the oval (photo 5). [....]

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