Ideal hyperbolic quadrilateral

An ideal hyperbolic quadrilateral is the region bounded by four hyperbolic geodesics whose four consecutive endpoints are distinct points on the ideal boundary. The ideal vertices lie outside the hyperbolic plane. In the hyperbolic disk, the four vertices $1,i,-1,-i$ give a regular example: its sides are the interior arcs of the circles of radius one centered at $\pm 1\pm i$. Although the sides have infinite length, the quadrilateral has finite hyperbolic area $2\pi$ in curvature $-1$.