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My question is the following: Are there triangulations of $S^3$ which (a) are non-degenerate, (b) have four vertices, and (c) have no edges of degree two? A side question: If one represents this ...

Stacked spheres A triangulation of a 2-dimensional sphere is called a stacked sphere if it is obtained inductively from the boundary of a 3-simplex by deleting a 2-face (triangle) $T$ adding a new ...