Creating a New Polyhedron from the Snub Dodecahedron

Shown below are the snub dodecahedron and its dual, the pentagonal hexecontahedron.

Seeking a way to make a “new” polyhedron (one never seen before), I augmented each face of the orange dual, above, with prisms. These prisms have a height equal to twice the average edge length of their bases.

Augmented Penta Hexeconta

Next, I used the software I use to manipulate polyhedra (Stella 4d, available here) to create the convex hull of this augmented pentagonal hexecontahedron.

starball before ttmfr expanded pentagonal hexacontahedron

Finally, I used Stella’s “try to make faces regular” function, and obtained this result, which I liked enough to stop here. There’s no way for me to know with certainty that this polyhedron has never been seen before, of course, but that didn’t stop me from having fun making it.

Unnamed starball.gif

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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2 Responses to Creating a New Polyhedron from the Snub Dodecahedron

  1. ejohn152 says:

    What would you be willing to bet that the rectangles in the convex shell are not a regular expression of tau?

    In other words, would you rule out [1+ squrt(5)]/2 as being involved. Until you do, the shell can be considered

    “regular” as is. I’m suggesting that the Golden Ratio would legitimize a claim of regularity; the final funtional

    operation’s result sure as hell doesn’t. Those of us with a knowledge of basic polyhedral geometry have no

    need for Stella 4d!

    ________________________________

    Like

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