The formation of a continuous crystal network in magmas and lavas can provide finite yield strength, tau_y, and thus can cause a change from Newtonian to Bingham rheology. The rheology of crystal-melt suspensions affects geological processes, such as ascent of magma through volcanic conduits, flow of lava across the Earth's surface, melt extraction from crystal mushes under compression, convection in magmatic bodies, or shear wave propagation through partial melting zones. Here, three-dimensional numerical simulations are used to investigate the onset of `static' yield strength in a zero-shear environment. Crystals can be approximated as convex polyhedra of any shape, size, and orientation. We determine the critical crystal volume fraction, phi_c, at which a crystal network first forms. The value of phi_c is a function of object shape and orientation distribution, and decreases with increasing randomness in object orientation and increasing shape anisotropy. For example, while parallel-aligned convex objects yield phi_c=0.29, randomly-oriented cubes exhibit a maximum phi_c of 0.22 and approximations of plagioclase crystals as randomly-oriented elongated and flattened prisms (tablets) with aspect ratios between 1:4:16 and 1:1:2 yield 0.08 < phi_c < 0.20. The dependence of phi_c on particle orientation implies that the flow regime and resulting particle ordering may affect the onset of yield strength. phi_c in zero-shear environments is a lower bound for phi_c. Finally the average total excluded volume concept is used, within its limitation of being a ``quasi-invariant'', to develop a scaling relation between tau_y and phi for suspensions of different particle shapes.