Sharp-eyed polyhedronists may wonder about the dodecahedron augmented with pentagonal pyramids, because it closely resembles the pentakis dodecahedron, which is one of the Catalan solids. I checked, though, and the red triangles’ angles are not quite correct for that designation.

I made this using Stella 4d, which you can try for free at http://www.software3d.com/Stella.php.