An invariant defined using the angles of a three-dimensional polyhedron. It remains constant under solid dissection and reassembly. Solids with the same volume can have different Dehn invariants. Two polyhedra can be dissected into each other only if they have the same volume and the same Dehn invariant. In 1902, Dehn showed that two interdissectable polyhedra must have equal Dehn invariants, settling the third of Hilbert's problems, and Sydler showed that two polyhedra with the same Dehn invariants are interdissectable.

dissection | Ehrhart polynomial | Hilbert's problems