Further Sprague-TThis preprint presents a rigorous three-dimensional analogue of Sprague's 1936 truncation for the Lebesgue universal covering problem. Starting from Kuperberg's truncated rhombic dodecahedron R_1, we identify six untouchable triangles on the boundary faces near the degree-four vertices A, C, E by means of the parallel-plane principle. These triangles locate the regions that can be safely removed. The three hexagonal faces F_1, F_2, F_3 remaining after Kuperberg's truncation are at distance exactly 1 from the three original rhombic faces. Any body of constant width 1 touching F_1 is contained in the set F_1 ⊕ B(0,1), a solid figure bounded by two parallel planes at distance 2, together with the lateral surfaces of six cylinders of radius 1 and spherical patches of radius 1 centred at the vertices of F_1. The portions of R_1 lying outside the intersection of the three such sets are therefore never occupied by a body touching all three faces and can be removed. We prove the universal covering property by a three-face contact argument based on local forced translation. The volume of the resulting body, estimated by Monte-Carlo integration, is 0.66895 ± 0.00001, a reduction of 0.39% from Kuperberg's record of 0.67157. The upload includes the preprint PDF and the accompanying source code (MATLAB visualization scripts and a Python script for Monte-Carlo volume estimation).ype Truncations of the Kuperberg Polyhedron for the Three-Dimensional Lebesgue Universal Covering Problem