# A Concave Polyhedron Featuring Eight Regular Dodecagons

This 110-faced polyhedron has, in addition to the eight regular dodecagons, six rectangles, and 96 triangles. I made it using Stella 4d, a program you can try for free, as a demo version, at http://www.software3d.com/Stella.php. I wish I could remember how I made it!

Fortunately, I have many friends who are more knowledgeable than I, when it comes to mathematics. Perhaps one of them will be able to solve this mystery.

## 8 thoughts on “A Concave Polyhedron Featuring Eight Regular Dodecagons”

1. Hi Robert,

Have you checked the Bilinski Rhombic Dodecahedron https://www.youtube.com/watch?v=xVBOlbjiHGI

Regards Jens

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On Mon, Aug 17, 2020 at 10:58 AM RobertLovesPi.net wrote:

> RobertLovesPi posted: ” This 110-faced polyhedron has, in addition to the > eight regular dodecagons, six rectangles, and 96 triangles. I made it using > Stella 4d, a program you can try for free, as a demo version, at > http://www.software3d.com/Stella.php. I wish I could remember ” >

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2. If the rectangles are not squares, then the triangles are isosceles, right? What are the relative dimensions of the sides?

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• I don’t even think the triangles are all congruent. Unfortunately, I did not save a .stel file for this polyhedron, so it’s a mystery — at least for now.

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3. However you did it, it turned out beautifully!

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On Mon, Aug 17, 2020 at 4:58 AM RobertLovesPi.net wrote:

> RobertLovesPi posted: ” This 110-faced polyhedron has, in addition to the > eight regular dodecagons, six rectangles, and 96 triangles. I made it using > Stella 4d, a program you can try for free, as a demo version, at > http://www.software3d.com/Stella.php. I wish I could remember ” >

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• Thank you!

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• I’m not sure, except that I know it would have tetrahedral symmetry.

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