Steven Dutch, Natural and Applied Sciences, University of Wisconsin  Green Bay
These are Schlegel Nets; that is, one face (usually the one with the most edges) has been selected as a base and the polyhedron flattened into a plane within the enclosing polygon. To help with identifying faces, they are colorcoded as follows:
Also, we are only concerned with topologically distinct polyhedra, that is, differing in number or type of faces and vertices. Thus, a triangular prism and a tetrahedron with one vertex truncated are topologically equivalent 5hedra, a cube and rhombohedron are topologically equivalent 6hedra, and so on.
General Notes on Polyhedron Enumeration
Three adjacent 45 edges, no 44 vertices
Two 44 edges 

Three adjacent 45 edges, one 44 vertex  
Three nonadjacent 45 edges
The first four have 2 44 edges, the last two have one 44 edge and two 44 vertices. 

Three nonadjacent 45 edges
one 44 edge and one 44 vertex.


Three nonadjacent 45 edges
one 44 edge 

Two adjacent 45 edges
One or more triangles enclosed by quadrilaterals 

Two adjacent 45 edges  
Two adjacent 45 edges  
Two adjacent 45 edges  
Two adjacent 45 edges  
Two nonadjacent 45 edges  
Two nonadjacent 45 edges  
Two nonadjacent 45 edges  
Two nonadjacent 45 edges  
Two nonadjacent 45 edges  
One 45 edge  
One (or no) 45 edge 
Return to Symmetry Index
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Created 10 June 1998, Last Update 19 September, 2015
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