There is a large stone polyhedron in Durer’s engraving Melencolia (1514), which is regarded as a truncated rhombohedron. Besides recognizing it as some symbol, the attempt to clarify its structure has been made. Since the polyhedron is drawn in perspective, we can identify the acute angle of the rhombuses, the faces of the rhombohedron before truncation, as about 80° by use of graphics. But the angle seems somehow not significant, like an angle 72° which is connected with the golden section. Now I set up a new hypothesis which confirms the significance of the polyhedron with an angle 80°. We see a vague figure on the largest pentagonal face of the polyhedron in the engraving which has been often recognized as a skull. I regard it as an anamorphic representation of a skull, and furthermore, the polyhedron as that of a truncated cube. Durer could have enlarged a correctly drawn cube vertically by “verkerer” in a certain ratio to draft a rhombohedron. And I regard the enlargement ratio as the solution to the duplication of a cube, the so-called Delian problem, which originated in ancient Greece. This famous problem in mathematics interested him and is described in his book.