Steven Dutch, Natural and Applied Sciences, University of Wisconsin - Green Bay
Heartbreak Hill. There are 198 of these, each with two possible base faces. The variations with pentagon-pentagon edges are shown with an auxiliary view where the pentagons are folded flat, making an octagon, and the other faces are shown. This approach frequently reveals topological similarities better than a mere Schlegel net view.
There are 12 polyhedra with no adjoining pentagons, 37 with pentagons joined at a vertex, and 149 with pentagons sharing an edge. In this set, since the pentagons account for all ten vertices, there are no others available. All the other faces must connect both pentagons.
Created 15 September 2015, Last Update 27 October 2015
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