There are plenty of other reptiles if you allow fractal reptiles. There are four examples of such reptiles in here.

One example is the dragon fractal.

For polygons, your examples are the only ones. For rational reptiles, (see reference) there are an additional four 2-reptiles for the plane, which are fractal. It is unknown if there non-rational 2-reptiles, but conjectured that there are none. A reptile is rational, if the rotations needed to get the two parts are all rational multiples of $\pi$ (if I am not mistaken).

There are plenty of other reptiles if you allow fractal reptiles. There are four examples of such reptiles in here (Wayback Machine).

One example is the dragon fractal.

For polygons, your examples are the only ones. For rational reptiles, (see reference) there are an additional four 2-reptiles for the plane, which are fractal. It is unknown if there non-rational 2-reptiles, but conjectured that there are none. A reptile is rational, if the rotations needed to get the two parts are all rational multiples of $\pi$ (if I am not mistaken).

There are plenty of other reptiles if you allow fractal reptiles. There are four examples of such reptiles in here.

One example is the dragon fractal.

For polygons, your examples are the only ones. For rational reptiles, (see reference) there are an additional four 2-reptiles for the plane, which are fractal.

There are plenty of other reptiles if you allow fractal reptiles. There are four examples of such reptiles in here.

One example is the dragon fractal.

For polygons, your examples are the only ones. For rational reptiles, (see reference) there are an additional four 2-reptiles for the plane, which are fractal. It is unknown if there non-rational 2-reptiles, but conjectured that there are none. A reptile is rational, if the rotations needed to get the two parts are all rational multiples of $\pi$ (if I am not mistaken).