Monday, November 21, 2011
Friday, November 18, 2011
Rhombic tessellations, as for example in anyam gila weaving, often create an illusion of stacked cubes. When the surface really does have that stacked-cube texture, as in some of Torolf Sauermann's parametric sculptures, it can be realized by weaving elements that have 90-degree bends; for example, bent strips of sheet metal. The weaving pattern is not that of the challenging, double-layered anyam gila, but simply open triaxial weave. The geometry of the bends closes up the hexagonal openings.
I liken it to a truss because the interwoven bends stiffen the surface against bending, like corrugating sheet metal.
The bends can be preformed on a two-pin jig. The distance between the outside of the pins needs to be slightly wider than the strip. Here, 0.59" for 0.50" x .017" steel strapping.
The stacked cubes pattern implicitly defines a 2-colorable triangulation:
The dual of the triangulation is a bipartite trivalent map:
Starting from any given map, M, a bipartite trivalent map is defined by the map operation bevel, Be(M). That new map describes a woven truss. The corresponding 2-colorable triangulation is given by Mt(M).
The weavers themselves follow along the edges of the medial of the triangulation, Me(Mt(M)), or, identically, Me(Be(M)).
Posted by James Mallos at 8:38 AM