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It is shown that 2-dimensional subdivisions can be made regular by moving their vertices within parallel 1-dimensional spaces. As a consequence, any 2-dimensional subdivision is projected from the boundary complex of a 4-polytope. ...
A polyhedral subdivision of a d-dimensional point configuration A is k-regular if it is projected from the boundary complex of a polytope with dimension at most d+k. Call γk(A) the subgraph induced by k-regular triangulations in the flip-graph of A. Gel’fa ...
Flip-graph connectedness is established here for the vertex set of the 4-dimensional cube. It is found as a consequence, that this vertex set admits 92487256 triangulations, partitioned into 247451 symmetry classes. ...