Display 4-dimensional objects is a challenge because of the extra dimension.
I proposed a method inspired by technical drawing https://hal.archives-ouvertes.fr/hal-03192641 to handle more easily 4-dimensional spaces.
Based on this idea, I used threejs to build Tak4d an online tool https://www.raktres.net/tak4d/ that shows two use-cases.
A 4D maze
Your are in a 4D labyrinth looking for an hypersphere. You see the 4D maze through four 3D views which are generated thanks to Threejs.
A short presentation is available in the video https://youtu.be/gU-HD63ahyM (switch on English subtitles)
There are tutorials and when you got it, you can try random mazes.
A viewer for 4D geometric scenes
The viewer take advantage of the 4 windows display to create and manage rather complex 4D scenes. It allows you to view scenes through projections or cuts, to add or move 4D solids. It’s very efficient to show lot of 4-dimensional euclidean geometry experiments.
Some presentation video are available on the playlist https://www.youtube.com/playlist?list=PLD5yLeJQ0t9jaMS5JX2JNoa2NN0_p05kK
For example, how to build a 4-dimensional box with Tak4D https://youtu.be/gHv2L5YNYvY
4D models are build with a specific algorithm, ADSODA created by Greg Ferrar (https://github.com/raktres/adsoda-js) and managed in the four 3D windows thanks to Threejs.