I created these three pieces using a geometric construction system called PolyPuzzle, which uses a programmed laser to precision-cut myriad shapes in high-quality colored paper. The system was invented by my friend and colleague James Ziegler. The seeds of this new method of working were planted a few years ago, when James and I were looking at my geometric paper constructions, some of which were exhibited at the 2005 Banff Bridges Conference. The availability of a stock of pre-cut pieces allows me freedom to experiment in a spirit of open-minded play with different combinations of shapes. While the PolyPuzzle system relies solely on locking-tabs, I have taken the liberty of moving beyond this system, creating new works, or modifying existing ones and augmenting with glued joints. Although these constructions come out of a knowledge of the basic geometric solids, PolyPuzzle has led me to surprisingly different structures – ones I may not have otherwise discovered.
The Super Sphere came out of experimentation with PolyPuzzle pieces. I discovered a module made of three hexagons (three edges curved) and three small triangles, and realized they could be connected in the manner of an icosidodecahedron. To fill the left-over, five-sided openings, I made the longer "bow-tie" pieces which connect the pentagons in the centre. The design evolved so that the bow-tie and isosceles triangle were combined into a single piece. This piece was sized to create a curved form with the set of hexagons. Aesthetically, the bow-tie pieces emphasize the pentagonal faces. I love spherical forms and the feeling of accomplishment I get when the last pieces are installed. Although this has a basic icosidodecahedral form, it is in fact quite unique. Does it fit any known geometric solid?
This spherical form is derived from a small rhombicuboctahedron and is constructed of 18 octagonal PolyPuzzle pieces with curved scoring in a square pattern. The colored inserts are each made of three rhombi to form a three-pointed star shape. As with the piece titled ‘180 Folded Hexagons’, this form required a high degree of skill and craftsmanship. The contrast between curved and straight-edged forms, and the interplay of overlapping circles, creates a compellingly aesthetic piece that invites the eye to trace the patterns and symmetry.
This piece of folded hexagons goes back to a discovery I made in 1969 about the possibilities of curved scoring in combination with regular and semi-regular geometric solids. It is made up of 180 hexagonal PolyPuzzle pieces with curved scoring in a triangular pattern. Because the inherent tension in the form tends to pull the joints apart, the internal joints are glued. The spherical form is a derivative of a truncated icosahedron and its intrinsic beauty is emphasized by the "flower of life" pattern in both the pentagons and hexagons.