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.
RobertLovesPi.net 
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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Wow! That is quite a video. I also found some more information on Bilinski’s rhombic dodecahedron here: https://en.wikipedia.org/wiki/Bilinski_dodecahedron.
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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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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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What does the convex hull look like?
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I’m not sure, except that I know it would have tetrahedral symmetry.
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