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Equidecomposability of polyhedra under cutting-and-pasting along faces, and generalizations. Hilbert's third problem, Dehn's invariants. Homological developments motivated by these issues.

21 votes
3 answers
929 views

Cutting of a regular polygon into congruent pieces

Question. For which $N$ it is possible to cut a regular $N$-gon into congruent pieces such that the center of the regular polygon lies strictly inside one of the pieces? For $N=3,4$ there are trivial …
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