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.
RobertLovesPi.net 
very pleasant to look at
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Thank you!
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This is very cool : D
Out of topic a bit. I need to tell you that the correct ratio of circumference of a circle divided by the diameter of the same circle is 4/sqrr(golden ratio) or about 3.144605511029693144278234343371835718
Do deep research on it and you will see the truth.
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Icosahedral symmetry?
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Yes.
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