A Twice-Zonohedrified Dodecahedron, Together with Its Dual

Zonohedrified Dodeca

This polyhedron was created by performing vertex-based zonohedrifications of a dodecahedron — twice. The first zonohedrification produced a rhombic enneacontahedron, various version of which I have blogged many times before, but performing a second zonohedrification of the same type was a new experiment. It has 1230 faces, 1532 vertices, and 2760 edges. All of its edges have equal length. I created the models in this post using Stella 4d, a program you can buy, or try for free, right here.

Here is the dual of this zonohedron, which has 1532 faces, 1230 vertices, and 2760 edges. This “flipping” of the numbers of faces and vertices, with the number of edges staying the same, always happens with dual polyhedra. I do not know of a name for the class of polyhedra made of zonohedron-duals, but, if any reader of this post knows of one, please leave this name in a comment.

Zonohedrified Dodeca dual

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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5 Responses to A Twice-Zonohedrified Dodecahedron, Together with Its Dual

  1. swo8 says:

    Very nice Robert.
    Leslie

    Liked by 1 person

  2. veezybell says:

    i think my brain just exploded.

    Liked by 1 person

  3. Anonymous says:

    Excelentes cuerpos geométricos son asombrosos, estarán los planos para construirlos

    Liked by 1 person

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