There are many polyhedra that include only hexagons and pentagons as faces — infinitely many, in fact. Most of the well-studied ones include twelve regular pentagonal faces, though, but this polyhedron has twenty-four pentagons, none of which are regular, in six panels of four pentagons each. Its regular faces are the eight hexagons, in the face-planes of the faces of an octahedron.
I made this with Stella 4d, software you can try here.
RobertLovesPi.net 
Stunning! Sort of hypnotic, too….
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This model is interesting. Do you know the angles of the pentagon as I think it may work well with other shapes.
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I wish I did, but I’d need this polyhedron’s .stel file to find that. If I kept .stel files for every polyhedron I post, I think they would fill my computer’s hard drive, plus every jumpdrive I own, so I generally don’t save them!
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