Compact asymmetric form in the plane?

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Not being a mathematician, I may be imprecise in asking my question. For experiments on the visual perception of symmetries in the plane, I'm looking for (a) a closed curve in the plane, that is (b) asymmetric (wrt rotation and reflection), and is (c) compact (as close as possible to the compactness of a circle), (d) minimizes points of inflexion. I thought that perhaps a half yin-yang would be a suitable candidate, but the question seems underdetermined.