Report on calculating room modes in rooms with curved walls

Report on calculating room modes in rooms with curved walls. I’ve done half the research but pretty sure a lot of it is wrong lol. The shapes I decided to compare the room modes in are triangles with both concave and convex curved walls, and squares with both concave and convex curved walls, as well as their straight edged equivalents. So what I need it some one to check my background research, calculate the room modes for each of the 6 shapes and discuss the results.