This symmetrohedron has four faces which are regular hexagons, 24 which are regular pentagons, and four which are equilateral triangles. It also has twelve faces which are acute isosceles triangles, as well as twelve more which are obtuse isosceles triangles. I made it using Stella 4d, which you can try for free here.
Here is its dual.
I made these using Stella 4d: Polyhedron Navigator, a program you may try for free at http://www.software3d.com/Stella.php.
This 31-faced polyhedron is unusual in that it features six regular heptagons as faces. I made it using Stella 4d, which you can try for free at this website.
This polyhedron is unusual in that it has five regular heptagons as faces. It has twenty-two faces in all. It was created using Stella 4d, software you can try for free right here.
To make this, I started with a dodecahedron, dropped the symmetry of the model from icosahedral to tetrahedral, then stellated it five times. Finally, I chose “color as a compound” for the color-settings. I did this using Stella 4d, software you can try for free right here: http://www.software3d.com/Stella.php.
Thanks and a tip of the hat to Livio Zucca, who gave me the idea for this tessellation.
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