To make this, I stellated the dual of the tetrated dodecahedron over 200 times, and then applied Stella 4d‘s “try to make faces regular” function. This is probably not the easiest method to use, but I don’t know of any others. The quadrilaterals are all kites.

If you’d like to give Stella a try, for free, the website to visit is http://www.software.com/Stella.php/