Three Polyhedra with Only Pentagonal Faces

72 pentagons

The polyhedron above has 72 pentagonal faces of two types. The next one below has three different types of pentagon for its 132 faces. After that is a polyhedron with sixty faces, all of which are non-convex pentagons.

132 pentagons

60 concave pentagons

All three of these all-pentagon polyhedra were created using Stella 4d: Polyhedron Navigator. This program is available here.

About RobertLovesPi

I go by RobertLovesPi on-line, and am interested in many things. The majority of these things 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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5 Responses to Three Polyhedra with Only Pentagonal Faces

  1. teachezwell says:

    They are all spectacular! Wish I could have them in hand.

    Liked by 1 person

  2. Pingback: * Three Polyhedra with Only Pentagonal Faces — RobertLovesPi’s Blog | Teachezwell Blog

  3. I love pentagons, although my preference is convex.
    Question, is it possible to have a polyhedron of 240 convex pentagons?
    I think it is, but I don’t have enough math background to determine if it is so.

    Liked by 1 person

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