In Unity, I have a RuleTile with a texture which is not rotationally symmetrical:

I want to make 3 other, similar tiles, where the texture is rotated 90°, 180° or 270°.

I could do that by making 3 other textures of the leftward, upward and downward facing triangles. It's not particularly nice to do that though as now if I ever change the texture I have to manually change all 4 orientations. I also now use 4x as much storage as I would for these textures (imagine I want to make a lot of different tiles, all of which are orientable).

Instead, I want to have 4 different rule tiles, which rely on a singular texture. Unless I'm missing something, I can't see a way to do this on a RuleTile. I wonder if it is possible to make a Custom Rule Tile Script which allows this behaviour.

Note that this is not the same thing as the following RuleTile behaviour:

This, on a single RuleTile type, causes a random orientation (left, right, up or down) to be chosen, relying on a single texture. Instead, I want 4 different RuleTile types, relying on a single texture, so that I can consistently paint where in the tilemap I want each orientation to appear.