Enneahedra with 10 vertices: 3333 444 55

Pentagons Not Adjacent

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.

General Notes on Polyhedron Enumeration

Return to Symmetry Index
Return to Polyhedra Enumeration Index
Return to Recreational Mathematics Index

Return to Professor Dutch's Home Page

Created 15 September 2015, Last Update 27 October 2015

Not an official UW Green Bay site