For my entry at the virtual JMM2021 Mathematical Art Exhibition.

Since you can't walk around these models to see them from different angles or pick them up and turn them over, I've made some animations. These are from the openscad IDE, not photos of the actual models, so I can use different colors for faces and edges.

Click on an image to run the animation. Each grows the slicing hyperplanes ax + by +cz + dw = N for N=1, ..., one slice at a time, rotates the finished model and then ungrows it in reverse order.

This is the most symmetrical figure: 2222. I filled some sample faces.

2233, with sample faces filled

The first nine slices of 2357. Can you see the first four primes?

The first six slices of 2225.

The python program hyperslices.py generates openscad code to customize for any particular model - for example, 2222animate.scad for the blue model.