Convex and discrete geometry Polytopes and polyhedra Concept
Dehn invariant
Summary
The Dehn invariant of a polyhedron combines the lengths of its edges with their dihedral angles in a tensor product of abelian groups. It does not change when a polyhedron is cut into pieces and the pieces are reassembled. Max Dehn used it in 1900 to solve Hilbert's third problem. A cube and a regular tetrahedron of the same volume have different Dehn invariants, so neither can be cut into the other.
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| Tag | S0TGRX3ARS |
|---|---|
| URI | m2://S0TGRX3ARS |
| Kind | concept |
| Writing | W0 stub |
| MSC | 52B45, 51M20 |
| Same as |
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