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Sydler pi/4 polyhedron (final)
All dihedral angles of this polyhedron are right except for one which is 45 degrees. The polyhedron is also scissors congruent to a cube.
This polyhedron has been described by Jean-Pierre Sydler in his proof of Sydler’s Theorem which is related to Hilbert’s third problem and states that every polyhedron is determined by its volume and Dehn invariant up to scissors congruence.
References: J.-P. Sydler, “Conditions necessaires et suffisantes pour l’equivalence des polyedres de l’espace euclidien a trois dimensions”, Commentarii mathematici Helvetici (1965/66) Volume: 40, page 43-80