Lenses within the schizochroal eyes of phacopine trilobites are made principally of calcite, and characterization of them using light microscopy and high-resolution electron imaging and diffraction has revealed an array of microstructural arrangements that suggest a common original pattern across the suborder. The low convexity lenses of Odontochile hausmanni and Dalmanites sp. contain calcite fibres termed trabeculae. The c axis of trabecular calcite lies parallel to the lens axis, and adjacent trabeculae are distinguished by small differences in their a axis orientations. Despite the common alignment, the boundaries between trabeculae cross-cut the c axis as they fan out towards the lens base. Trabeculae are absent from the lens immediately beneath the visual surface, and instead, a radial fringe is present and is composed of micrometre-thick sheets of calcite whose c axes are oriented at a low angle to the visual surface. High convexity lenses are more common than those of lower convexity among the species studied, and they have a much thicker radial fringe. Beneath this fringe, all of the lens calcite is oriented with its c axis parallel to the lens axis and it lacks trabeculae. We propose that both the high and low convexity lenses formed by rapid growth of calcite from a surface that migrated inwards from the cornea, and they may have had an amorphous calcium carbonate precursor. The trabeculae and radial fringes are unlikely to have had any beneficial effect on the transmission or focusing of light, but rather are the outcomes of an elegant solution to the problem of how to construct a biconvex lens from a crystalline solid.