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Title: Seifert Surface of the Trefoil
Artist and Designer: Matthew Wright
Materials: Acrylic yarn and wire
Artist’s Statement: If you take a strip of paper, twist it once and a half, and tape the ends together, the surface you get will have the trefoil knot as its boundary. But is there an orientable surface—one with two diﬀerent sides—that has the trefoil as its boundary? And in general, what knots or links are the boundary of some orientable surface? It turns out that they all are: we can always ﬁnd an orientable surface (in fact, many) with a given knot or link as its boundary. Such surfaces are called Seifert surfaces, and they are a useful tool in knot theory.