This polyhedron is an example of a zonohedron — a polyhedron with faces which are all zonogons, each of which is congruent and parallel to another zonogon on the opposite side of the polyhedron.
Of course, this just raises the question, “What’s a zonogon?” It’s a special type of polygon, one with an even number of sides, and with opposite sides congruent and parallel.
The pulsating effect is just for fun — a feature which is optional in Stella 4d, the program I used to make this. I started with an icosahedron/dodecahedron compound, stellated it many times, and then zonohedrified the result. This software makes all these operations easy, and may be tried for free at http://www.software3d.com/stella.php.