Is there another kind of two-dimensional geometry? I learned that in two-dimensional geometry, there are Euclidean geometry, hyperbolic geometry and spherical geometry. These geometries are homogeneous and isotropic. Is there another kind of two-dimensional geometry that is homogeneous and isotropic?

In addition to the nine following a specific set of rules,
There are also more exotic versions such as projective geometry (think twisting the plane into a Mobius strip) and finite geometries.
If you relax the isotropic requirement you open up more possibilites such as the Manhattan metric aka Taxicab Geometry.
