Materials with significant porosity, generally termed cellular solids, exhibit unique properties unachievable by their solid counterparts. These characteristics, which may include ultra-low density, high surface area per unit volume, and/or improved impact absorption, are greatly influenced by both the degree of open porosity and the physical arrangement of the solid material within the cellular structure. Ordered cellular structures generally exhibit superior stiffness and peak strength relative to random cellular configurations by changing the mode of deformation within the microstructure during elastic loading.[ [6] However, these techniques are not well suited for fabricating mesoscale structures [7] with feature sizes ranging from tens to hundreds of micrometers. Here we present a new class of cellular structures formed from a three-dimensional interconnected pattern of self-propagating polymer waveguides. In contrast to existing lithographic techniques, [3][4][5][8][9][10][11] , this self-propagating effect enables the rapid formation (< 1 min) of thick (> 5 mm) three-dimensional open-cellular structures from a single two-dimensional exposure surface. The process also affords significant flexibility and control of the geometry and configuration of the resulting cellular structure, which in turn, provides control of the bulk physical and mechanical properties.A self-propagating polymer waveguide can be formed from a single point exposure of light in a suitable photomonomer and can yield a high-aspect-ratio polymer fiber (length/diameter > 100) in seconds with approximately constant cross-section over its entire length. [12,13] This self-propagating phenomenon is a result of a self-focusing effect caused by a change in the index of refraction between the liquid photomonomer and solid polymer during the polymerization reaction. [12][13][14] Upon exposure of light in the appropriate wavelength range -typically UV for most photosensitive monomers -polymerization begins at the point of exposure and the subsequent incident light is trapped in the polymer because of internal reflection, as in optical fibers. This self-trapping effect tunnels the light towards the far end of the already-formed polymer, further propagating the polymerization front within the liquid monomer.[15] The diameter of the waveguide is dependent on the exposed area, and the length is primarily dependent on the incident energy of the light and the photo-absorption properties of the polymer. [16] Eventually, the polymer itself will absorb enough light in the critical wavelength range to terminate waveguide propagation. Previous studies on waveguide formation utilized a fiber optic, lens apparatus, or focusing mask to create a point source of light which initiated the formation of the self-propagating polymer fiber through the monomer. [12][13][14][15][16] However, asshown in the present work, this effect can be achieved using a broad spectrum collimated light source (generated from a mercury arc lamp) directed through a mask with a simple circu...