Sydler pi/4 polyhedron (final)

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All dihedral angles of this polyhedron are right except for one which is 45 degrees. The polyhedron is also scissors congruent to a cube. See entire construction. This polyhedron has been described by Jean-Pierre Sydler in his proof of Sydler's Theorem, which relates 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 necessary and sufficient for the equivalence of three-dimensional Euclidean space polyhedra," Commentarii Mathematici Helvetici (1965/66) Volume 40, page 43-80