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Neural style transfer (NST), where an input image is rendered in the style of another image, has been a topic of considerable progress in recent years. Research over that time has been dominated by transferring aspects of color and texture, yet these factors are only one component of style. Other factors of style include composition, the projection system used, and the way in which artists warp and bend objects. Our contribution is to introduce a neural architecture that supports transfer of geometric style. Unlike recent work in this area, we are unique in being general in that we are not restricted by semantic content. This new architecture runs prior to a network that transfers texture style, enabling us to transfer texture to a warped image. This form of network supports a second novelty: we extend the NST input paradigm. Users can input content/style pair as is common, or they can chose to input a content/texture-style/geometry-style triple. This three image input paradigm divides style into two parts and so provides significantly greater versatility to the output we can produce. We provide user studies that show the quality of our output, and quantify the importance of geometric style transfer to style recognition by humans.