Polyhedron Featuring Decagons and Pentagons

Polyhedron Featuring Decagons and Pentagons

There are twelve regular decagons in this polyhedron, and sixty irregular pentagons. If the pentagons were closer to regularity, this would qualify as a near-miss to the ninety-two Johnson Solids. It is not known how many of these “near-misses” exist — primarily because this group of polyhedra lacks a precise definition.

This polyhedron was discovered with the aid of Stella 4d, software you can try for yourself at http://www.software3d.com/stella.php.

2 thoughts on “Polyhedron Featuring Decagons and Pentagons

    • After seeing your question, I tried to recreate this polyhedron using Stella 4d, and got very close to it. I started with the truncated dodecahedron, and augmented its twelve decagonal faces with antiprisms. Next, I formed the convex hull, and stellated it once. Finally, I tried to use Stella’s “try to make faces regular” function to finish the job, but this didn’t work. My other recourse would be to adjust the height of the antiprisms by trial and error, and that would take a while.

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