The graph obtained by replacing the faces of a polyhedron with its edges and vertices is therefore the skeleton of the polyhedron. The polyhedral
graphs corresponding to the skeletons of Platonic solids
are illustrated above. The number of topologically distinct skeletons with graph vertices for , 5, 6, ... are 1, 2, 7, 18, 52, ... (OEIS A006869).
-skeleton is a simplicial
subcomplex of 
that is the collection of all simplices of 
of dimension at most 
, denoted 
.
with 
graph vertices for 
, 5, 6, ... are 1, 2, 7, 18, 52, ... (OEIS A006869).
