Editing Polycube (section)

==Dual graph==
The structure of a polycube can be visualized by means of a "dual graph" that has a vertex for each cube and an edge for each two cubes that share a square.<ref>{{citation
 | last1 = Barequet | first1 = Ronnie
 | last2 = Barequet | first2 = Gill
 | last3 = Rote | first3 = Günter
 | doi = 10.1007/s00493-010-2448-8
 | issue = 3
 | journal = Combinatorica
 | mr = 2728490
 | pages = 257–275
 | title = Formulae and growth rates of high-dimensional polycubes
 | volume = 30
 | year = 2010| s2cid = 18571788
 | citeseerx = 10.1.1.217.7661
 }}.</ref> This is different from the similarly-named notions of a [[dual polyhedron]], and of the [[dual graph]] of a surface-embedded graph.

Dual graphs have also been used to define and study special subclasses of the polycubes, such as the ones whose dual graph is a tree.<ref>{{citation
 | last1 = Aloupis | first1 = Greg
 | last2 = Bose | first2 = Prosenjit K. | author2-link = Jit Bose
 | last3 = Collette | first3 = Sébastien
 | last4 = Demaine | first4 = Erik D. | author4-link = Erik Demaine
 | last5 = Demaine | first5 = Martin L. | author5-link = Martin Demaine
 | last6 = Douïeb | first6 = Karim
 | last7 = Dujmović | first7 = Vida | author7-link = Vida Dujmović
 | last8 = Iacono | first8 = John | author8-link = John Iacono
 | last9 = Langerman | first9 = Stefan | author9-link = Stefan Langerman
 | last10 = Morin | first10 = Pat | author10-link = Pat Morin
 | contribution = Common unfoldings of polyominoes and polycubes
 | doi = 10.1007/978-3-642-24983-9_5
 | mr = 2927309
 | pages = 44–54
 | publisher = Springer, Heidelberg
 | series = Lecture Notes in Comput. Sci.
 | title = Computational geometry, graphs and applications
 | volume = 7033
 | year = 2011| hdl = 1721.1/73836
 | isbn = 978-3-642-24982-2
 | url = http://cg.scs.carleton.ca/%7Evida/pubs/papers/Cubigami.pdf
 }}.</ref>