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Reconstruction of slices of cubes
Marie-Charlotte Brandenburg, Juliana Curtis, Chiara Giardino, Chiara Meroni, Arnau Padrol
Source abstract
We prove that the combinatorial type of a slice of the cube by a hyperplane is completely determined by its graph, within the class of cube slices. We also show that such a result cannot extend to slices of arbitrary simple polytopes by constructing a simple polytope that has two combinatorially distinct slices with isomorphic graphs.
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