Enneahedra with 9 vertices:
faces 333 334 445

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 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

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.

Three non-adjacent 4-5 edges

one 4-4 edge and one 4-4 vertex.

 

Three non-adjacent 4-5 edges

one 4-4 edge 

Two adjacent 4-5 edges

One or more triangles enclosed by quadrilaterals

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 19 September, 2015

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