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For applications in computing, Bézier curves are pervasive and are defined by a piecewise linear curve L which is embedded in R 3 and yields a smooth polynomial curve C embedded in R 3 . It is of interest to understand when L and C have the same embeddings. One class of counterexamples is shown for L being unknotted, while C is knotted. Another class of counterexamples is created where L is equilateral and simple, while C is self-intersecting. These counterexamples were discovered using curvedoi:10.4995/agt.2012.1624 fatcat:7r7k227f4fbb5gcrzjct5nbh34