Using Steve Hollasch's thesis on extension of perspective projection/viewing matrix into 4D to visualize 4D objects.
I didn't actually successfully get this going, so I ended up doing a simple "smear" (translate by w in x and y to stretch the object out in 3D space) to visualize as the project deadline was looming and I had other finals to study for. This was a lot of fun though, I'll be back to poke at it.
I'm fairly certain my hypercube generation is wrong, but I didn't want to change it because it looked cooler this way and this was more of an artistic project.