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.

3 thoughts on “A Polyhedron with Eight Regular Hexagonal Faces and Twenty-Four Irregular Pentagonal Faces

    • 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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