Here's my webgl project https://filbs111.github.io/3sphere-explorer/
PC recommended. Controls don't work on mobile.
It's more a game "engine" than a game at the moment.
The main gimmick of the engine is that you fly around "inside" a 3-sphere. Basically it's similar to being constrained to a 2D world on the surface of a sphere, but +1 dimension. You're confined to a "3D" space consisting of the set of 4D points some fixed distance from a 4D origin. Because shaders as standard deal in 4-vectors, 4x4 matrices, implementation is quite neat - it's mainly just using 4-vectors for vertex properties and appropriate transformations in the vertex shader. If it runs slow on your machine it'll be because it's doing a lot more. The core rendering of this kind of space using GL doesn't require any heavy lifting.
Drawing of all regular polytopes is implemented. Currently it initially displays a 600-cell. You can toggle others. See "polytopes" menu. To see these better, you may wish to set atmosphere contrast to 0. menu: display->atmosContrast
The engine supports repeating rectangular terrains mapped onto duocylinders. This works out neatly - you don't have to worry about the player flying off the map, or invisible walls, and can use a simple tiles for map editing. Many older games have repeating square maps, that I remember fondly. For example Virus/Zarch, Zeewolf, V2000. The duocylinders can be spun, like an O'Neill cylinder, to create gravity. You can switch terrain options in menu: drawShapes:world0/1
The secondary gimmick is spherical portals, joining different 3-sphere worlds together. Currently engine only has one per world, so limit of 2 worlds, but plan to permit 3 portals per world so can have a web of worlds.
The player controls are probably too complicated at the moment. Click and drag on screen to rotate, or tap 'f' to go fullscreen so mouse rotates spaceship directly. WASD, \, space move spaceship. Or you can use a gamepad.
TODO list includes performance and graphics improvements, Collision, restitution mechanics, more vehicles, gameplay objectives. Improved terrain, map editor.
I should put together better instructions or tutorial video, but another day. Have a go if you want!