In geometry, the Dehn invariant is a value used to determine whether one polyhedron can be cut into pieces and reassembled ("dissected") into another,...

have Dehn invariant zero. The Dehn invariant has also been connected to flexible polyhedra by the strong bellows theorem, which states that the Dehn invariant...

the same Dehn invariant. He then shows that every cube has Dehn invariant zero while every regular tetrahedron has non-zero Dehn invariant. Therefore...

been named for Dehn. Among them: Dehn's rigidity theorem Dehn invariant Dehn's algorithm Dehn's lemma Dehn plane Dehn surgery Dehn twist Dehn–Sommerville...

changing continuously. Connelly conjectured that the Dehn invariant of a flexible polyhedron is invariant under flexing. This was known as the strong bellows...

Rozansky–Witten invariant Vassiliev knot invariant Dehn invariant LMO invariant Turaev–Viro invariant Dijkgraaf–Witten invariant Reshetikhin–Turaev invariant Tau-invariant...

any other polyhedron of the same volume using polyhedral pieces (see Dehn invariant). This process is possible, however, for any two honeycombs (such as...

of the 20th century—Max Dehn, J. W. Alexander, and others—studied knots from the point of view of the knot group and invariants from homology theory such...

also give rise to invariants of 3-manifolds via the Dehn surgery construction. These invariants were discovered by Nicolai Reshetikhin and Vladimir Turaev...

same zones, and with one parallelepiped for each triple of zones. The Dehn invariant of any zonohedron is zero. This implies that any two zonohedra with...