A Polyhedron Featuring 180 Kites as Faces, Plus Related Polyhedra

If one starts with the great rhombicosidodecahedron, then makes a compound of it, and its dual, and then forms the convex hull of that compound, this is the result:

180 kites 60&60&60

This polyhedron has 180 faces, all of them kites. What’s more, there are equal numbers — sixty each — of the three different types of kites in this polyhedron.

It also has an interesting dual:

180 kites 60&60&60 the dual

These virtual polyhedral models were created using Stella 4d: Polyhedron Navigator, which you can buy, or try for free, right here. Stella contains a “try to make faces regular” function, and here is what appears if that operation is applied to the dual shown above:

180 kites dual with TTMFR

The dual of this figure is similar to the original polyhedron at the top of this post, featuring 180 kites, again: sixty each, of three different types:

180 kites with TTMFR

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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