are geometric models constructed from interlocking sets of planar pieces. The basic idea behind sliceform construction is indicated in the pair of photos below. By creating two sets of slotted pieces ("slot-from-the-top" and "slot-from-the-bottom" sets) that intersect at right angles, one can link the two sets together to form attractive models of surfaces and solids.

Sliceforms are described briefly in Cundy and Rollett's brilliant compendium "Mathematical Models". The best recent references on the subject are by the British mathematician/artist John Sharp, whose books "Sliceforms" and "Surfaces" include numerous beautiful examples done in colored paper.

We are working on a software application called "Sliceform Creator" whose purpose is to help children create sliceform models in paper, wood, or plastic with the aid of a desktop laser cutter. The basic idea behind the program is that the user can specify a wide range of solid forms and surfaces (like the paraboloid shown in the figure at left), and the software will produce a set of sliceform pieces (like the wooden pieces shown in the upper part of the figure) that can be assembled into full-scale models. Sliceform Creator can also be used with a color printer or computer-controlled paper cutter to make paper sliceform models.