This symmetrohedron’s regular faces are twelve pentagons, thirty octagons, and twenty triangles. Its irregular faces include sixty yellow isosceles trapezoids, as well as sixty blue isosceles trapezoids. That makes 182 faces in all.

I used *Stella 4d: Polyhedron Navigator* to make this, and you can try this program yourself, as a free trial download, at http://www.software3d.com/Stella.php.

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