AWhat changed
Dehn established a necessary angle relation for finite polyhedral dissection into congruent pieces and proved that a regular tetrahedron cannot be reassembled into a prism, even when their volumes agree.
Scientific scope
Dehn established a necessary angle relation for finite polyhedral dissection into congruent pieces and proved that a regular tetrahedron cannot be reassembled into a prism, even when their volumes agree. The obstruction concerns finite dissections of polyhedra into the stated class of pieces, preserving volume and the relevant angle/length invariant. Equal volume alone does not guarantee that such a dissection exists. This is not a prohibition of every infinite decomposition or arbitrary nonmeasurable construction. Hilbert presented the paper; that does not make him its coauthor.
Evidence
Source-linked, scoped account of the original work. The published scope states the scientific assumptions and remaining verification limits. WRS has not independently certified the full proof, experimental result or system benchmark.
Contributors
- M. Dehn · SCIENCE: Original source-listed scientific author of this scoped work; byline does not determine effort fractions.
- M. Dehn, Ueber raumgleiche Polyeder (1900) — original 10 page article
- R. Bricard, Sur une question de geometrie relative aux polyedres (1896) — originalprecursor
- Pierre Cartier, Decomposition des polyedres (1986) — partiallaterreview
Provisional WRS assessment, edition 2026-10-16.1. Independent expert calibration is pending. This grade does not certify correctness or assign ownership.
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