Periodic

Periodic subdivisions are composed of a limited number of different cells (often a small number) that repeat themselves through isometric transformations so that they fill the stereotomic surface. A direct application from two dimensional tilings to three dimensional surfaces is possible if the stereotomic intrados (or extrados) surfaces are developable such as the cone, cylinder, or any generalized cylinder with constant radius and straight axis (Ballard and Brown, 1982).

On another note, this kind of subdivision only allows for a modular production of voussoirs if not only all the intrados are the same, but also if the contact surfaces angles and extrados are the same, and this is dependent on a constant curvature of the surface; the only surfaces of the three dimensional euclidian space which bear constant principal curvature “must be a round sphere or a tube over a regular curve” (Anciaux, 2013, p. 1), such as is the case of the HyparVault.