This is joint work with Henry Segerman (www.shapeways.com/shops/henryseg). It models a regular space-filling tessellation of hyperbolic space (one of eleven exotic tessellations that have infinite cells and/or vertex figures). In this case, the cell is a tiling of squares, and the model is face-centered. Four cells meet at every edge, and an infinite number of cells meet at every vertex (the vertex figure is a tiling of squares too). For more details, see Coxeter's paper, "Regular Honeycombs in Hyperbolic Space"