Puzzles and polytope isomorphisms
The authors call the set \(\pi\) \({\mathfrak C}\) of d- and (d-1)-cells of a simplicial d-complex \({\mathfrak C}\) its puzzle, and a puzzle isomorphism between two such complexes \({\mathfrak A},{\mathfrak B}\) is a bijection between \(\pi\) \({\mathfrak A}\) and \(\pi\) \({\mathfrak B}\) which preserves dimension and incidence. They use homological arguments to show that puzzle isomorphisms between the boundary complexes of simplicial polytopes extend to combinatorial isomorphisms between the polytopes, thus confirming (in the dual form) a conjecture of Perles.
scientific article; zbMATH DE number 4032501