  The taxicab plane is a modification of the Euclidean plane that uses an
alternative notion of distance. Similarly, the Poincar\'{e} disk is a model of
hyperbolic geometry that consists of a subset of the Euclidean plane with an
alternative notion of distance. In this paper, we merge these two variations to
create a taxicab version of the Poincar\'{e} disk in an attempt to create a
type of taxicab hyperbolic space.
