  Recent studies in magnetic nanolithography show that a variety of complex
magnetic states emerge as a function of a single magnetic island's aspect
ratio. We propose a model which, in addition to fitting experiments, predicts
magnetic states with continuous symmetry at particular aspect ratios and
reveals a duality between vortex and vertex states. Our model then opens new
means of engineering novel types of artificial spin systems, and their
application to complex magnetic textures in devices and computing.
