Dürer's solid is one of only four well-covered simple convex polyhedra.

[2] The exact geometry of the solid depicted by Dürer is a subject of some academic debate, with different hypothetical values for its acute angles ranging from 72° to 82°.

As well as its construction as the skeleton of Dürer's solid, it can be obtained by applying a Y-Δ transform to the opposite vertices of a cube graph, or as the generalized Petersen graph G(6,2).

[5] The Dürer graph is Hamiltonian, with LCF notation [-4,5,2,-4,-2,5;-].

[6] More precisely, it has exactly six Hamiltonian cycles, each pair of which may be mapped into each other by a symmetry of the graph.