This polyhedron combines the faces of an icosidodecahedron (red and blue) with the those of a rhombic triacontahedron (green). The gaps between those two sets of polygons are the yellow rectangles. I made this using the “morph duals by expansion” function of Stella 4d: Polyhedron Navigator. You can try this program for yourself, free of charge, at http://www.software3d.com/Stella.php.
RobertLovesPi.net 
Is there a name for this polyhedron? I had this in mind but it’s the only example I can find when I searched 30 rhombi, 60 rectangles, 12 pentagons and 20 triangles. I suppose there are infinite variations if you keep the golden rhombi and vary the dimensions of the rectangles.
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There’s no name that I know of. The title of the post was my attempt at one.
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THIS HYBRID SHAPE IS… …PERFECT!!!!!!!!!!!!!!!!
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