In this paper, a new convex polyhedron is introduced, obtained by systematically truncating all 24 edges of a rhombic dodecahedron such that the newly generated 24 congruent vertices lie exactly on a common spherical surface. The resulting truncated rhombic dodecahedron is a non-uniform convex polyhedron composed of 12 congruent rectangular faces, 6 congruent square faces, and 8 congruent equilateral triangular faces, with a total of 48 edges and 24 identical vertices. Using HCR’s Theory of Polygon, closed-form analytical expressions are derived for the radius of the circumscribed sphere passing through all vertices, the normal distances of the rectangular, square, and equilateral triangular faces from the center of the polyhedron, as well as its total surface area and enclosed volume. In addition, analytical formulae are obtained for the solid angles subtended at the center by each type of face, the dihedral angles between any two faces meeting at each of the 24 vertices, and the solid angle subtended by the truncated rhombic dodecahedron at each of its vertices.