Original: The half-plane model is identical (at the limit) to the Poincaré disc model at the edge of the disc The Lorentz model or hyperboloid model employs a 2-dimensional hyperboloid of revolution (of two sheets, but using one) embedded in 3-dimensional Minkowski space.
Simplified: The half-plane model is identical (at the limit) to the Poincaré disc model at the edge of the disc This model has direct application to special relativity, as Minkowski 3-space is a model for spacetime, suppressing one spatial dimension.