The plots shown to the right use the first equation. Hypars We use the term hypar to mean a hyperbolic paraboloid shape, or more formally a partial hyperbolic paraboloid, cut from the full infinite surface. We are particularly interested in how hypars can be joined together at their edges to make interesting sculpture. Hypars in Architecture Hypars and joining hypars in a few special ways have been used extensively in architecture. It is amazingly easy to fold a hypar from a square piece of paper.
More detailed diagrams are available.
One method, which we call a k-hat , is to glue k hypars together in a kind of ring. We call these structures hyparhedra . Please refer to the paper below for details on the algorithms. For now, this page just contains photographs of a few examples. Please refer to this paper for more details on the above subject.