This polyhedron can be constructed by truncating two opposite vertices of a cube, of a trigonal trapezohedron (a convex polyhedron with six congruent rhombus sides, formed by stretching or shrinking a cube along one of its long diagonals), or of a rhombohedron or parallelepiped (less symmetric polyhedra that still have the same combinatorial structure as a cube).

In the case of a cube, or of a trigonal trapezohedron where the two truncated vertices are the ones on the stretching axes, the resulting shape has three-fold rotational symmetry.

The shape of the solid depicted by Dürer is a subject of some academic debate.

[1] According to Lynch (1982), the hypothesis that the shape is a misdrawn truncated cube was promoted by Strauss (1972); however most sources agree that it is the truncation of a rhombohedron.

Despite this agreement, the exact geometry of this rhombohedron is the subject of several contradictory theories: