Here are a couple quick videos of the 120 cell made for your enjoyment using 120 Cell Explorer. The animations show how the appearance of this object would change as we rotate our viewpoint around it in 4D.
Both show half of the 120 cells and color the cells based on which "ring" they are on. The highly symmetric 120 cell can be thought of as composed of 12 rings of 10 cells each, hence these animations are showing 6 of the 12 rings. One ring (the purple one) is more difficult to see because it is surrounded by the 5 others. All of the rings are linked to every other ring exactly once, so unless you were a magician, you couldn't pull any 2 of the rings apart without breaking one of them. Can you see the linking?
The next video is slightly more interesting to me. It is essentially identical to the first one except that we are starting from a different vantage point in 4D.