Steven Dutch, Professor Emeritus, 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 color-coded 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 5-hedra, a cube and rhombohedron are topologically equivalent 6-hedra, and so on.
General Notes on polyhedron Enumeration
Three adjacent 4-5 edges, no 4-4 vertices
Two 4-4 edges |
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Three adjacent 4-5 edges, one 4-4 vertex | |
Three non-adjacent 4-5 edges
The first four have 2 4-4 edges, the last two have one 4-4 edge and two 4-4 vertices. |
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Three non-adjacent 4-5 edges
one 4-4 edge and one 4-4 vertex.
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Three non-adjacent 4-5 edges
one 4-4 edge |
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Two adjacent 4-5 edges
One or more triangles enclosed by quadrilaterals |
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Two adjacent 4-5 edges | |
Two adjacent 4-5 edges | |
Two adjacent 4-5 edges | |
Two adjacent 4-5 edges | |
Two non-adjacent 4-5 edges | |
Two non-adjacent 4-5 edges | |
Two non-adjacent 4-5 edges | |
Two non-adjacent 4-5 edges | |
Two non-adjacent 4-5 edges | |
One 4-5 edge | |
One (or no) 4-5 edge |
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Created 10 June 1998, Last Update 11 June, 2020