Horosphere
![A horosphere within the Poincaré disk model tangent to the edges of a hexagonal tiling cell of a hexagonal tiling honeycomb](/Images/godic/202502/01/633_honeycomb_one_cell_horosphere1738.png")
![Apollonian sphere packing can be seen as showing horospheres that are tangent to an outer sphere of a Poincaré disk model](/Images/godic/202502/01/Apollonian_spheres1739.jpg")
In hyperbolic geometry, a horosphere (or parasphere) is a specific hypersurface in hyperbolic n-space. It is the boundary of a horoball, the limit of a sequence of increasing balls sharing (on one side) a tangent hyperplane and its point of tangency. For n = 2 a horosphere is called a horocycle.