This is a tesselation of hyperbolic space with cubes.

When cubes tesselate "normal" 3D space, there are four cubes around each edge. In this hyperbolic tesselation, there are 5.

Mathematicians use this symbol to denote a cube: {4,3}. That's because it has square faces (that's why the 4 is there) and there are three per corner (that's why the 3 is there)

The tesselation of "normal" space with cubes would be {4,3,4}; the {4,3...} because it's a tesselation by cubes, and the last '4' because there are 4 per edge.

The tesselation you're looking at in this link is {4,3,5}.

There are three other tesselations of hyperbolic space with platonic solids: if you explored {5,3,4}, each room would be a dodecahedron, and there'd be 4 per edge. It's related to the {4,3,5} by "duality"; the same way the cube is related to the octahedron.

You can also fit five (larger) dodecahedrons around each edge, to get {5,3,5}.

The last one is {3,5,3}, a tesselation of icosahedra, with three around each edge.

I'd love to see an app that let you explore these others.

Note that if you're exploring hyperbolic space, it's really, really easy to get lost, since paths that deviate even slightly in direction rapidly move further and further apart. If you want to retrace your steps, you need to retrace them incredibly carefully.