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I hate you Mordant.
Crag The Mandelbrot set as both chaos and Mandelbrot are kinda overrated. Pretty just isn't enough.
Shag The Moebius strip, because imagine the interesting things you can do after you cut it in half to find two interlocked strips. Not a bag because there are boundary issues that will doubtless lead to a lack of closure. (That was a math joke, btw. If this was a math crowd, you'd all be in stitches. Oh, kill me now.)
Bag The Klein bottle cos its one of my favorite non-orientable two dimensional real riemannian manifolds. With a description like that, whats not to love?
An immersed Klein bottle:
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