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Abstract
In this paper, it is demonstrated that every 3-colorable knot diagram corresponds to a canonical 3-ball, referred to as a "butterfly," featuring topologically reflected faces. Additionally, it is established that this ball can be triangulated using a 4-color scheme that aligns with the knot's 3-coloring. Consequently, a corollary emerges, associating at least one of these specialized balls with any given 3-manifold.
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References
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