For every knot K in the 3-sphere, there exists a one-vertex triangulation of S^3 with an edge that forms K, with an explicit construction from any diagram of K.
Burton, Ryan Budney, Will Pettersson, et al., Regina: Software for 3-manifold topology and normal surface theory , http://regina-normal.github.io/, 1999–2023
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Triangulations of the 3-sphere with knotted edge
For every knot K in the 3-sphere, there exists a one-vertex triangulation of S^3 with an edge that forms K, with an explicit construction from any diagram of K.