Before revision:  This Hilbert geometry naturally yields a generalization of the Klein disk model of hyperbolic geometry, which we term the Siegel-Klein  model to differentiate it with the usual Siegel upper plane and Siegel disk domains.
After revision:  This Hilbert geometry naturally yields a generalization of the Klein disk model of hyperbolic geometry, which we term the Siegel-Klein model to differentiate it with the classic Siegel upper plane and Siegel disk domains.