A Polyhedron with Eight Regular Hexagonal Faces and Twenty-Four Irregular Pentagonal Faces

8 reg octs and 16 irreg pents

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.

About RobertLovesPi

I go by RobertLovesPi on-line, and am interested in many things, a large portion of which are geometrical. Welcome to my little slice of the Internet. The viewpoints and opinions expressed on this website are my own. They should not be confused with the views of my employer, nor any other organization, nor institution, of any kind.
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3 Responses to A Polyhedron with Eight Regular Hexagonal Faces and Twenty-Four Irregular Pentagonal Faces

  1. teachezwell says:

    Stunning! Sort of hypnotic, too….

    Liked by 1 person

  2. Dave Smith says:

    This model is interesting. Do you know the angles of the pentagon as I think it may work well with other shapes.

    Liked by 1 person

    • 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!

      Like

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