This solid has all the faces of the great rhombicosidodecahedron, plus 120 scalene triangles. I made it using Stella 4d, which you can try for free right here.
A Symmetrohedron Derived From the Great Rhombicosidodecahedron
RobertLovesPi.net
Polyhedra, tessellations, and more.
RobertLovesPi.net 
very relaxing!
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I am a geometric artist with a very solid algebraic foundation and consider myself a math nerd. It seems my understanding and conceptualization of projective geometry are superficial at best, whereas before I subscribed to your content I had held as not half bad. Attempting to wrap my mind around the principle of duality isn’t being met with much success this morning, I’m afraid.
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Duality is hard to understand fully. I’m not all the way there, myself.
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