| Einstein “Special Relativity” (ESR) | von Brzeski “Special Relativity” (BSR) |

Lobachevskian Real 3-dim Space | $SL\left(2C\right)/SU\left(2\right)$ Quotient of Lorentz Group | $SL\left(2C\right)/SU\left(2\right)$ Quotient of Lorentz Group |

Type of Lorentz Group Action on $SL\left(2C\right)/SU\left(2\right)$ | Single sided (left) $x=g{x}^{\prime}$ | Double sided $x={g}^{\mathrm{*}}{x}^{\prime}g$ |

Type of Projection (Type of Map) | Gnomonic (central), non-conformal | Stereographic, conformal |

Type of Coordinates | Projective Weierstrass | Projective rational |

Resulting Model of Lobachevskian Geometry | Beltrami-Klein, non-conformal | Poincare, conformal |

Relation between BSR and ESR | Isomorphic as models, Homotopic as maps | Isomorphic as models, Homotopic as maps |