In the first case we have a dome, or a portion of one, covering a square apartment; in the second we have the same covering standing on arches open towards the exterior; in the third, we have a dome covering the intersection of two barrel-vaults, just as is more usually done by groining.
The process, however, is not limited to a square; it is equally applicable to the octagon or any other polygon—indeed, to any figure which can be inscribed in a circle.
The following diagrams (Figs. [407], [408], and [409]) will tend better to explain this.
Nor is it necessary that the inscribed figure should be complete, for remnants of the circle may equally well be left between the arches or walls.
Fig. 407.
Fig. 408.