Bridges 2012 Short Paper
Building the Schwarz D-Surface from Paper Tiles
(Proceedings pages 373–376)
Periodic minimal surfaces are doubly curved and so problematic to
create from paper, a material more amenable to developable surfaces.
However, breaking the curvature into polygonal facets can visually
approximate these surfaces. Furthermore, repeating and alternately
inverting a single fundamental patch will tile periodic surfaces.
This patch may be triangulated and unfolded into patterns for the
modeler to print and fold into a number of non-planar tiles for
constructing the surface. In the case of a lined periodic minimal
surface, like the Schwarz D-Surface, the straight lines crisscrossing
the surfaces define the boundaries of the fundamental patch as
non-planar polygons. As demonstrated in this paper, such saddle
polygons are relatively simple to fabricate and then to join into
a representation of the surface.