Geodesic
Dürer polyhedra: the dark side of melancholia
Discussiones Mathematicae. Graph Theory, Tome 22 (2002) no. 1, pp. 101-109

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Dürer's engraving Melencolia I famously includes a perspective view of a solid polyhedral block of which the visible portion is an 8-circuit bounding a pentagon-triple+triangle patch. The polyhedron is usually taken to be a cube truncated on antipodal corners, but an infinity of others are compatible with the visible patch. Construction of all cubic polyhedra compatible with the visible portion (i.e., Dürer Polyhedra) is discussed, explicit graphs and symmetries are listed for small cases ( ≤ 18 vertices) and total counts are given for 10 ≤ vertices ≤ 26.
Keywords: graph theory, geometry, chemistry 
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Fowler, Patrick; John, Peter. Dürer polyhedra: the dark side of melancholia. Discussiones Mathematicae. Graph Theory, Tome 22 (2002) no. 1, pp. 101-109. http://geodesic.mathdoc.fr/item/DMGT_2002_22_1_a7/