The 5 solids are the Tetrahedron, Cube, Octahedron, Dodecahedron, and Icosahedron.

The original developer of Mainframe protected each servers' Repo with a Private Key hidden inside one of the solids.

Once you have the code for a server, you can apply Mods to the game, like being able to replay it as a Nuzlocke, Speedrun, Challenge mode etc.