  We observe capillary-driven binding between thin, equilateral triangular
prisms at a flat air-water interface. The edge length of the equilateral
triangle face is 120 $\mu m$, and the thickness of the prism is varied between
2 and 20 $\mu m$. For thickness to length (T/L) ratios of 1/10 or less, pairs
of triangles preferentially bind in either a tip-to-tip or tip-to-midpoint edge
configurations; for pairs of particles of thickness T/L = 1/5, the tip of one
triangle binds to any position along the other triangle's edge. The distinct
binding configurations for small T/L ratios result from physical bowing of the
prisms, a property that arises during their fabrication. When bowed prisms are
placed at the air-water interface, two distinct polarity states arise: prisms
either sit with their center of mass above or below the interface. The
interface pins to the edge of the prism's concave face, resulting in an
interface profile that is similar to that of a capillary hexapole, but with
important deviations close to the particle that enable directed binding. We
present corresponding theoretical and numerical analysis of the capillary
interactions between these prisms and show how particle bowing and contact-line
pinning yield a capillary hexapole-like interaction that results in the two
sets of distinct, highly-directional binding events. Prisms of all T/L ratios
self-assemble into space-spanning open networks; the results suggest design
parameters for the fabrication of building blocks of ordered open structures
such as the Kagome lattice.
