This is the snub cube. It’s one of the thirteen Archimedean solids.
The first modification I made to this polyhedron was to stellate it once.
The next step was to augment each yellow face with a tall prism.
Next, I formed the convex hull of the above solid.
The software I use to manipulate polyhedra, Stella 4d, has a function called “try to make faces regular.” The last step of this short polyhedral journey was to use this function on the above convex hull.
If you would like to try Stella 4d for yourself, there is a free trial download available at http://www.software3d.com/Stella.php.