This is a 600-cell, one of the regular polychora (four-dimensional polytopes), with its edges and vertices rendered invisible, and its cells shrunk so that they do not touch. It’s rotating in hyperspace, and what you are seeing at any given moment is a particular three-dimensional “shadow,” or projection, of the entire figure.

It’s easy to make this sort of thing with software called Stella 4d, written by an Australian friend of mine. Here’s a link to a site where you can try it, as a free trial download, before deciding whether or not to purchase the fully-functioning version: http://www.software3d.com/Stella.php.